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Which recursive formula can be used to define this sequence for n>1n > 1?\newline5,18,31,44,57,70,5, 18, 31, 44, 57, 70, \ldots\newlineChoices:\newline(A) an=an113a_n = a_{n-1} - 13\newline(B) an=an1+13a_n = a_{n-1} + 13\newline(C) an=185an1a_n = \frac{18}{5}a_{n-1}\newline(D) an=an1+an113a_n = a_{n-1} + a_{n-1} - 13

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline5,18,31,44,57,70,5, 18, 31, 44, 57, 70, \ldots\newlineChoices:\newline(A) an=an113a_n = a_{n-1} - 13\newline(B) an=an1+13a_n = a_{n-1} + 13\newline(C) an=185an1a_n = \frac{18}{5}a_{n-1}\newline(D) an=an1+an113a_n = a_{n-1} + a_{n-1} - 13
  1. Sequence Type: We have the sequence: 5,18,31,44,57,70,5, 18, 31, 44, 57, 70, \ldots\newlineIs the given sequence geometric or arithmetic?\newlineThe difference between consecutive terms appears to be constant.\newlineThe given sequence is likely arithmetic.
  2. Find Common Difference: Find the common difference, dd, by subtracting two consecutive terms.\newlineFor example, take the second term and subtract the first term: 185=1318 - 5 = 13\newlineCommon difference (dd): 1313
  3. Identify Recursive Formula: Identify the recursive formula for the given sequence.\newlineSince the common difference is 1313, the recursive formula will involve adding 1313 to the previous term.\newlineThe recursive formula should be of the form: an=a(n1)+da_n = a_{(n-1)} + d\newlineSubstitute 1313 for dd in the formula.\newlineRecursive formula: an=a(n1)+13a_n = a_{(n-1)} + 13

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