Algebra & Trigonometry (10th Edition)
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3, 5, 7, 9 ; The term is .Substitute in and ... more
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1, ; The term is Substitute in and obtain the ... more
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6, 7, 8, 9, 10 ; The terms are ,, where . ... more
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1, 3, 4, 7, 11 ; The terms are , , and , where . ... more
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2, 4, 5, , ; The term is . Substitute in and ... more
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; Simplify the expression using the definition ... more
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; Obtain the sum . ; more
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Infinite sequence ; A function or a collection of ... more
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Finite ; A function or a collection of elements ... more
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Recursively ; A function or a collection of ... more
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Factorial ; Let be any positive integer. Then, ... more
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Index of summation ; The sum of the first terms is... more
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Series ; The sum of terms of finite or infinite ... more
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-3, 1, 5, 9, 13 ; The term is . Substitute in ... more
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5,3,5,3,5 ; Substitute 1 and 2 for in to find ... more
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2,0,2,0,2 ; Substitute 1 and 2 for in to find ... more
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-2, 4, -8, 16, -32 ; Substitute 1 and 2 for in ... more
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; Substitute 1 and 2 for in to find the first ... more
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; The function is independent of . This implies ... more
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6,-6,6,-6,6 ; Substitute 1 and 2 for in to find ... more
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,9, ; Substitute 1 and 2 for in to find the ... more
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1, ; Substitute 1 and 2 for in to find the first... more
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; Substitute 1 and 2 for in to find the first ... more
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3, ; Substitute 1 and 2 for in to find the first... more
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0, 0, 6, 24, 60 ; Substitute 1 and 2 for in to ... more
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-5, -4, 9, 40, 95 ; Substitute 1 and 2 for in to... more
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; Substitute 1 and 2 for in to find the first ... more
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; Substitute 1 and 2 for in to find the first ... more
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-73 ; It is observed that . Substitute 25 for in... more
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-240 ; It is observed that . Substitute 16 for in... more
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. ; It is observed that . Substitute 11 for in ... more
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; It is observed that . Substitute 13 for in to... more
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Perform the following operations on the graphing ... more
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Perform the following operations on the graphing ... more
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Perform the following operations on the graphing ... more
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Perform the following operations on the graphing ... more
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Perform the following operations on the graphing ... more
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Perform the following operations on the graphing ... more
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Find the first and tenth term of the sequence by ... more
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; Write the values of and the corresponding ... more
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; The term of the sequence is 1 less than the ... more
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; The term of the sequence is 2 more than the ... more
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; Each term of the sequence is 9 less than the ... more
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; The odd terms of the sequence are 1 and the ... more
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; Each term of the sequence is either 1 or 3, ... more
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; Keep 1 and 2 constant in the numerator and ... more
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; The denominator is increasing in the powers of ... more
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; The numerator is 1 more than the previous term... more
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; The numerator is a series of numbers with the ... more
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; The denominators of the terms of the sequence ... more
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; The terms of the sequence are increasing ... more
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; The numerators are in the form of powers of 3 ... more
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; The numerators of the sequence are increasing ... more
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28, 24, 20, 16, 12 ; Use the recursive relation to... more
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3,4,6,10,18 ; Let ,,,, and be the first five ... more
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81,27,9,3,1 ; Let ,,,, and be the first five ... more
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14, -28, 56, -112, and 224 ; Use the recursive ... more
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1, 2, 2, 3, and ; The initial five terms of any ... more
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-1, 1, 0, 1, 1 ; The initial five terms of any ... more
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1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and 1441, 2... more
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Use the relation and write the relation for . Now... more
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5, 5, , , and ; Expand to find the first five ... more
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1, , , , and ; Expand to find the first five ... more
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6, -24, 60, -120, and 210 ; Expand to find the ... more
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-1,,, and ; Expand to find the first five terms ... more
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; If there is any positive integer then the ... more
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495 ; If there is any positive integer then the ... more
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; If there is any positive integer then the ... more
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; If there is any positive integer then the ... more
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90 ; For any sequence, the sum of first terms can ... more
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40. ; For any sequence, the sum of first terms ... more
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. ; For any sequence, the sum of first terms can ... more
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25. ; For any sequence, the sum of the first ... more
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88. ; For any sequence, the sum of the first ... more
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238. ; Apply property of sum. ; Simplify the ... more
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. ; Simplify the expression by substituting values... more
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. ; Simplify the expression by substituting values... more
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; Use the summation functionality of the graphing... more
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; Use the summation functionality of the graphing... more
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1.33 ; Use the summation functionality of the ... more
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4468.625 ; Use the summation functionality of the ... more
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. ; Let the index of the summation be .The lower ... more
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. ; Let the index of the summation be .The lower ... more
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. ; Let the index of the summation be .The lower ... more
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. ; Let the index of the summation be .The lower ... more
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; Let the index of the summation be .The lower ... more
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; Let the index of the summation be .The lower ... more
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; Let the index of the summation be .The lower ... more
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; Let the index of the summation be .The lower ... more
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; Let the index of the summation be .The lower ... more
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; To write the sum in the summation notation, ... more
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; To find the desired sum, expand the summation ... more
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; To find the desired sum, expand the summation ... more
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. ; The sum is calculated by expanding the terms ... more
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. ; The sum is calculated expanding the terms of ... more
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True. The summation function follows the additive ... more
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True. The terms of the sequence on both the sides ... more
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; The number of accounts . Substitute... more
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Consider the expression and use the properties of... more
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Consider the expression . Apply the formula and ... more
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; The second term in the expansion should beThus... more
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The first term is missing. ; The total term after... more
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; ; ; ; 3 ; Let the term of the arithmetic ... more
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; For an arithmetic sequence with term as and ... more
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; The term of the arithmetic sequence can be ... more
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79 ; The and terms of the arithmetic sequence ... more
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217 ; Total number of terms in the sequence is 7 ... more
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43,560 ; The and terms of the arithmetic ... more
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1470 ; The and terms of the arithmetic sequence ... more
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2500000 ; The annual sales form an arithmetic ... more
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arithmetic ; In an arithmetic sequence, the ... more
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; For an arithmetic sequence with the first term... more
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recursion ; For an arithmetic sequence with the ... more
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finite arithmetic sequence ; For a finite ... more
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No ; Each term of the sequence is double the ... more
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Yes;5 ; The difference between any two consecutive... more
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Yes;-2 ; The difference between any two ... more
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No ; Each term of the sequence is half the ... more
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Yes; ; The difference between any two consecutive ... more
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Yes;-0.7 ; The difference between any two ... more
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No ; A sequence of square terms cannot be ... more
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Yes; ; The value of is 0, is approximately 0.693... more
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8, 11, 14, 17, 20;Arithmetic sequence;3 ; ... more
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97, 94, 91, 88, 85;Arithmetic sequence;-3 ; ... more
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7, 3, -1, -5, -9; Arithmetic sequence;-4 ; ... more
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1, 3, 7, 13, 21;Not an arithmetic sequence ; ... more
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-1, 1, -1, 1, -1;Not an arithmetic sequence ; ... more
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2,1, 4, 3, 6;Not an arithmetic sequence ; ... more
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2, 8, 24, 64, 160;Not an arithmetic sequence ; ... more
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Not arithmetic. ; To find the first five terms of... more
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; The formula for the term is of the form , ... more
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; The formulae for the term is of the form , ... more
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; The formula for the term is of the form , ... more
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; The formula for the term is of the form , ... more
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; Calculate the common difference between any ... more
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; Calculate the common difference between any ... more
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. ; The term of the arithmetic sequence is . ... more
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; Substitute and in the general equation of the... more
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; Substitute in the general equation for the ... more
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; Substitute in the general equation for the ... more
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; The term of an arithmetic sequence can be ... more
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; The term of an arithmetic sequence can be ... more
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; Use the values of and to calculate the common... more
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; Substitute in the general equation for the ... more
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; Substitute in the general equation for the ... more
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; Substitute in the general equation for the ... more
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; Determine the common difference by comparing ... more
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; Determine the common difference by comparing ... more
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. ; Determine the common difference by comparing ... more
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; Find the term using the recursion formula .... more
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-49 ; Substitute the value of in the recursion ... more
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83 ; Substitute the value of in the recursion ... more
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; Substitute the value of in the recursion ... more
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-92.4 ; Substitute the value of in the recursion ... more
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110 ; Substitute the number of terms in the ... more
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70. ; Substitute the number of terms in the ... more
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-25 ; Substitute number of terms in the sequence... more
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0 ; Substitute number of terms in the sequence, , ... more
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10000. ; Substitute the number of terms in the ... more
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-4550 ; Substitute number of terms in the sequence... more
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15100 ; Substitute the value of in the recursion ... more
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19200 ; Substitute the value of in the recursion ... more
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-7020 ; Substitute the value of in the recursion ... more
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375 ; Substitute the value of in the recursion ... more
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1275 ; The partial sum of a finite arithmetic ... more
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26425 ; The partial sum of a finite arithmetic ... more
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129250 ; The partial sum of a finite arithmetic ... more
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218625 ; The partial sum of a finite arithmetic ... more
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-28300 ; The partial sum of a finite arithmetic ... more
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33525 ; The partial sum of a finite arithmetic ... more
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The graph of and is a straight line and the ... more
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Find the values of to from the given line ... more
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Find the values of to from the given line ... more
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Find the values of to from the given line ... more
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Find the values of to from the given line ... more
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2430 ; The arithmetic sequence is with the common... more
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203. ; The first row of wall has one-half brick ... more
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784 ; The falling pattern of the object is an ... more
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; To find the total sales during the first , find... more
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The terms of this sequence contain the first term ... more
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True.Use the equation , where is the difference ... more
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True.The partial sum for the nth series could be ... more
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Use the first two terms to find the common ... more
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; The nth term of the sequence implies , where ... more
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. ; The nth term of sequence implies where is ... more
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The errors are and . ; The sum of the first 50 ... more
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-12, 24, -48, 96.-2. ; A geometric sequence has an... more
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2, 8, 32, 128, 512 ; If a geometric sequence has ... more
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104.2 ; Find the term of a geometric sequence ... more
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; Determine the common ratio using the formula . ... more
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; Express the relation between and . ; Compute ... more
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2.6664 ; Express the term as the sum of individual... more
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; Use the formulae for compound interest , where... more
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Geometric. ; The sequence is geometric when there... more
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; Since the common ratio of the geometric ... more
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; The sum of a finite geometric sequence which ... more
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Geometric series. ; The sum of an infinite ... more
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Geometric; ; A sequence is geometric if the ratio ... more
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Not geometric. ; A sequence is geometric if the ... more
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Geometric; . ; A sequence is geometric if the ... more
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Geometric; . ; A sequence is geometric if the ... more
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Not geometric. ; A sequence is geometric, if the ... more
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Geometric; ; A sequence is geometric if the ratio ... more
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Not geometric. ; A sequence is geometric if the ... more
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Geometric; . ; A sequence is geometric if the ... more
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; Apply the formula of term, i.e., to find the... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Apply the formula of term, i.e., to find the ... more
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; Substitute and in the formula to obtain the ... more
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. ; Substitute and in the formula to obtain the... more
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; Substitute and in the formula to obtain the ... more
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. ; Substitute and in the formula to obtain the... more
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; Substitute and in the formula to obtain the ... more
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; Substitute and in the formula to obtain the ... more
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; Substitute and in the formula to obtain the ... more
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; Substitute and in the formula to obtain the ... more
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; Substitute and in the formula to obtain the ... more
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; Substitute and in the formula to obtain the ... more
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; The sequence is geometric in nature with the ... more
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; The general term in a geometric series is ... more
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; The general term in a geometric series is ... more
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; The general term in a geometric series is ... more
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; The general term in a geometric series is ... more
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; The general term in a geometric series is ... more
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13122 ; Any term in a geometric series can be ... more
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20480 ; Any term in a geometric series can be ... more
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; Any term in a geometric series can be written ... more
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; Any term in a geometric series can be written ... more
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9 ; The common ratio of a geometric sequence can ... more
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12 ; The common ratio of a geometric sequence can ... more
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-2 ; The common ratio of a geometric sequence can ... more
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; The common ratio of a geometric sequence can be... more
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The first three terms in the sequence are 18, 12, ... more
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The first 10 values of the sequence given by the ... more
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The first 10 values of the sequence given by the ... more
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The first 10 values of the sequence given by the ... more
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5461 ; Expand the finite sum to obtain the first ... more
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113.33 ; The finite sum is expanded, and the first... more
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-14706 ; Comparing with provides the first term... more
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; Comparing with provides the first term , the ... more
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; The given series can be written as, Comparing ... more
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12.5 ; The given series can be written as ... more
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; The given function can be written as Comparing... more
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; The given function can be written as ... more
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1.6 ; The given function can be written as ... more
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45 ; The given function can be written as . ... more
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; By comparing the sequence with the standard ... more
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; By comparing the sequence with the standard ... more
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; By comparing the sequence with the standard ... more
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. ; The number of terms in the sequence is 5, ... more
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2 ; Comparing the standard form with results the... more
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8 ; Comparing the standard form with results the... more
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; Compare with results the first term and the ... more
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; Compare with results in the first term and ... more
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5 ; Compare with results the first term and the... more
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5 ; Compare with results with the first term ... more
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32. ; By comparing the sequence with the standard ... more
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27 ; By comparing the sequence with the standard ... more
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No sum. ; By comparing the sequence with the ... more
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No sum ; By comparing the sequence with the ... more
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; Express the repeating decimal in an infinite ... more
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; Express the repeating decimal as an infinite ... more
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The curve is asymptotic to the line and the sum of... more
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The curve is asymptotic to the line and the sum of... more
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; The machine is worth and it depreciates at the... more
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Compare the sequence with the standard sum of ... more
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Approximately ; Let the sum of the infinite ... more
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; The tax rebate is and the rate is which can ... more
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; The tax rebate is and the rate is which can ... more
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approximately ; Considering the side of the ... more
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; Initially, the ball was dropped from a height... more
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; The salary for the first year is , and there is... more
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False. The ratio of consecutive terms should be ... more
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False. The term is the common ratio to the power... more
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The next term in the geometric sequence can be ... more
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Proof:Prove the formula for .Assume that the ... more
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Proof:Prove the formula for .Assume that the ... more
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Proof:Assume that the inequality is true for .... more
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Proof:Assume that the formula is true for .Prove ... more
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To prove its validity, mathematical induction is... more
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; The quadratic model has the form . Substitute ... more
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Mathematical induction. ; The first step in ... more
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First. ; First differences are the difference ... more
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Arithmetic. ; Arithmetic sequences are defined by ... more
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Second. ; A perfect quadratic model is when the ... more
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; Determine the statement for the given by ... more
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; Determine the statement for the given by ... more
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; Determine the statement for the given by ... more
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; Determine the statement for the given by ... more
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; Determine the statement for the given by ... more
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; Determine the statement for the given by ... more
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Rewrite the given expressionWhen , the statement ... more
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Rewrite the given expression When , the ... more
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Rewrite the given expression When , the ... more
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Rewrite the given expression When , the ... more
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Rewrite the given expression When , the statement ... more
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Rewrite the given expression When , the statement ... more
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Rewrite the given expressionWhen , the statement ... more
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Rewrite the given expression When , the statement ... more
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Rewrite the given expression When , the statement ... more
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Rewrite the given expression When , the statement ... more
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Consider the given expression. Show the above ... more
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Consider the given statement.For , show that the ... more
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Consider the given statement. For , show the above... more
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The mathematical expression is same as The ... more
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Consider the inequality as a statement. Show the ... more
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Consider inequality as a statement.Show this ... more
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Consider inequality as a statement. Show the ... more
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Consider the inequality as a statement. Show the ... more
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Consider inequality as a statement. Show the ... more
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Consider the inequality as a statement. Show the ... more
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Consider a statement : is divisible by 3 for all... more
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Consider a statement : is divisible by 2 for all... more
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Consider a statement : is divisible by 3 for all... more
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Consider a statement : is divisible by 5 for all... more
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Consider a statement : for all . Show the ... more
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Consider a statement : for all .Show the ... more
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Consider a statement : , when for all . Show ... more
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Consider a statement : , when for all . Show ... more
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Consider a statement : for all . Show the ... more
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Consider a statement :'' and are complex ... more
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Proof:The number in an arithmetic sequence is ... more
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Proof:The number in a geometric sequence is given... more
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. Proof: Write first few sums of the given series ... more
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Proof:Write the first few sums of the given ... more
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120 ; The sum of the first positive integer is . ... more
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465 ; The sum of the first positive integer is . ... more
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91 ; The sum of squares of first integers is . ... more
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3025. ; The sum of cubes of first integers is . ... more
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979 ; The sum of fourth power of first integers ... more
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61776 ; The sum of fifth power of first integers ... more
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70 ; Distribute the summation over the addition in... more
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43890 ; Distribute the summation over the addition... more
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-3402 ; Distribute the summation over the addition... more
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195 ; Distribute the summation over the addition ... more
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Linear model; ; Find the first difference of the ... more
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Linear model; ; Find the first difference of the ... more
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Quadratic model; ; Find the first difference of ... more
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Quadratic model; ; Find the first difference of ... more
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Quadratic model; ; Find the first difference of ... more
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Quadratic model; ; Find the first difference of ... more
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The first difference is 3.The second difference is... more
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. ; Let the quadratic model be in the form . ... more
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; Let the quadratic model be in the form . ... more
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; Let the quadratic model be in the form . ... more
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; Let the quadratic model be in the form . ... more
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. ; Let the quadratic model be in the form . ... more
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; Let the quadratic model be in the form . ... more
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; Let the linear model be . Substitute in to ... more
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False; must be proven to be true. ; If the series ... more
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Consider an example of a sequence with terms.The ... more
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; Take the eighth row of Pascal's triangle. The ... more
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; In the fourth row of Pascal's triangle, the ... more
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; In the third row of Pascal's triangle, the ... more
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Expanding. ; The binomial is solved by expanding ... more
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Binomial coefficient. ; The binomial is solved by ... more
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Binomial theorem. ; The binomial is solved by ... more
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; The binomial is solved by expanding the ... more
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10 ; Using the definition of a binomial ... more
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7 ; Using the definition of a binomial coefficient... more
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1 ; Using the definition of a binomial coefficient... more
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1 ; Using the definition of a binomial coefficient... more
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210 ; Using the definition of a binomial ... more
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210 ; The binomial coefficient can be evaluated ... more
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4950 ; The binomial coefficient can be evaluated ... more
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4950 ; The binomial coefficient can be evaluated ... more
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20 ; Binomial coefficients can be obtained by ... more
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6 ; Binomial coefficients can be obtained by ... more
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5 ; Binomial coefficients can be obtained by ... more
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35 ; Binomial coefficients can be obtained by ... more
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; The binomial theorem helps expand the ... more
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; The binomial theorem helps expand the ... more
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; The binomial theorem helps expand the ... more
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; The binomial theorem helps expand the ... more
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; The binomial theorem helps expand the ... more
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; The binomial theorem helps expand the ... more
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; The binomial theorem helps expand the ... more
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; The binomial theorem helps expand the ... more
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; The expression is expanded using the binomial ... more
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; The expression is expanded using the binomial ... more
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; The expression is expanded using the binomial ... more
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; The expression is expanded using the binomial ... more
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; The expression is expanded using the binomial ... more
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; To expand an expression using Pascal's ... more
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. ; To expand an expression using Pascal's ... more
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. ; In a binomial expansion , the term is given ... more
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160 ; In a binomial expansion , the term is given... more
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-160 ; In a binomial expansion , the term is ... more
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720 ; The given binomial expression is , hence, .... more
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180. ; The given binomial expression is ,hence, .... more
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-6,300,000 ; The given binomial expression is ; ... more
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326592 ; For the binomial expression, , .For the ... more
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210 ; For the binomial expression, , .For the term... more
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45 ; For the binomial expression, , .For the term... more
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; Below is the general formula for the binomial ... more
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; Below is the general formula for the binomial ... more
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; Below is the general formula for the binomial ... more
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. ; The general formula for the binomial expansion... more
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; Below is the general formula for the binomial ... more
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; Below is the general formulae for the binomial ... more
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; For the given function , the expression is .... more
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-4 ; The general formula for the binomial ... more
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1 ; The coefficients from the third row of Pascal'... more
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1.171 ; The expression is rewritten as to ... more
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1049.89 ; The expression is rewritten as to ... more
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510568.785 ; The expression is rewritten as to ... more
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467.72 ; The expression is rewritten as to ... more
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0.27 ; The term is evaluated using the knowledge ... more
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0.25 ; The term is evaluated using the knowledge ... more
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0.27 ; The term is evaluated using the knowledge ... more
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is shifted towards the positive x axis by 3 units... more
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Fibonacci seriesThe sum of numbers in the ... more
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3 ; Count the different number of ways to obtain a... more
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2 ; Count the different number of ways to obtain a... more
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27,000 ; There are three events involved in this ... more
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24 ; There are 4 letters, W, X, Y, and Z.The ... more
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6 ; The odd integers between 1 and 12 are 1, 3, 5... more
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6 ; The even integers from the numbers 1 to 12 are... more
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5 ; The prime integers from numbers 1 to 12 are 2... more
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3 ; The integers from 1 to 12 that are divisible ... more
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4 ; The integers from 1 to 12 divided by three are... more
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252 ; One earthworm can be selected from among 9 ... more
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64 ; Consider six questions that are to be ... more
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4096 ; Consider twelve questions that are to be ... more
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5760000 ; The English alphabet contains 26 letters... more
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120 ; The number of permutations of elements is ... more
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720 ; The number of permutations of elements is ... more
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20 ; The number of permutations of elements, ... more
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720 ; The number of permutations of elements, ... more
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132 ; The number of permutations of elements, ... more
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720 ; The number of permutations of elements, ... more
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2730 ; Select the permutation function of the ... more
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94109400. ; Select the permutation function of the... more
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5527200 ; Select the permutation function of the ... more
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30240 ; Select the permutation function of the ... more
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504 ; In a family of 9 members, there are 9 ... more
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336 ; Among 8 sprinters, there are 8 ways to come ... more
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ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, ... more
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15 ; The number of combinations of elements taken... more
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5 ; The number of combinations of elements taken... more
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1 ; The number of combinations of elements taken... more
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1 ; The number of combinations of elements taken... more
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120 ; Select the combination function of the ... more
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6188 ; Select the combination function of the ... more
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4418694267732600 ; Combination of elements taken... more
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292600 ; The number of ways to choose 1 person A ... more
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35 ; The number of vertices in the decagon is ... more
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2 ; Simplify the given equation using the formula ... more
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0.5. ; A coin is tossed three times. The possible ... more
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0.76 ; There are a total of 52 playing cards in a ... more
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0.11 ; There are a total of 52 playing cards in a ... more
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0.69 ; There are a total of 52 playing cards in a ... more
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0.13 ; A six-sided dice is tossed twice. The ... more
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0.41. ; A six-sided dice is tossed twice. The ... more
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0.91 ; A six-sided dice is tossed twice. The ... more
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0.11 ; A six-sided dice is tossed twice. The ... more
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0.33 ; A six-sided dice is tossed twice. The ... more
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0.52 ; A six-sided dice is tossed twice. The ... more
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0.73 ; The total possible choices in the bag are... more
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0.47 ; Let be the event, which represents a ... more
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6,12,20,30,42 ; Substitute 1, 2, and 3 for in the... more
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4, 21, 38, 55, 72 ; The nth term of an arithmetic ... more
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45450. ; Let the arithmetic sequence be 9,18,27,36... more
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2805. ; Substitute , , and d=1 in to find the ... more
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80. ; Substitute the value of from 1 to 10 in ... more
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52. ; Substitute the value of from 1 to 8 in , and... more
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88. ; Split the terms of addition since the ... more
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250. ; The expression will lead to an arithmetic ... more
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676. ; Find the difference between the items ... more
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2, 30, 450, 6750, 101250. ; The general term of a ... more
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127. ; Obtain the first and the second term of the... more
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121. ; Obtain the first and the second term of the... more
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31. ; The given sum can be rewritten as which is... more
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24.96. ; The given sum, is of the form . The ... more
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12110. ; The sum of and for the first terms can... more
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Perfect linear model. ; The given sequence and ... more
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15. ; The expression represents the product of ... more
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220. ; The expression represents the product of ... more
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21. ; Pascal's triangle implies that the first ... more
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210. ; Pascal's triangle implies that the first ... more
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6. ; The possible outcomes from the system, such ... more
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72 ; The possible ways of selecting the first ... more
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120 ; There are 5 different ways of injecting the ... more
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720 ; There are 10 drivers in the race such that ... more
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225792840 ; The expression represents that ... more
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70. ; The expression represents the product of ... more
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462 ; The expression represents that the product ... more
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151200 ; The total number of letters in A,N,T,A,R,... more
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Consider that person A is running at a speed of , ... more
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1, 1.5, 1.4176, 1.4142, 1.4142, 1.4142, 1.4142, 1.... more
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In the process of mathematical induction, the ... more
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Length of the side at the stage: .Total area at ... more
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; The summation of the daily wages for 30 days is... more
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; If is the event that an answer from the ... more
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; Since the dart is equally likely to hit the ... more
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