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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=an1+an213a_n = a_{n-1} + a_{n-2} - 13\newline(B)an=an113a_n = a_{n-1} - 13\newline(C)an=an1+13a_n = a_{n-1} + 13\newline(D)an=185an1a_n = \frac{18}{5}a_{n-1}

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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=an1+an213a_n = a_{n-1} + a_{n-2} - 13\newline(B)an=an113a_n = a_{n-1} - 13\newline(C)an=an1+13a_n = a_{n-1} + 13\newline(D)an=185an1a_n = \frac{18}{5}a_{n-1}
  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 is the same.\newlineThe given sequence is 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. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSince the sequence is arithmetic, the recursive formula will have the form an=an1+da_n = a_{n-1} + d.\newlineSubstitute 1313 for dd in the formula.\newlineRecursive formula: an=an1+13a_n = a_{n-1} + 13
  4. Match with Choices: Match the recursive formula with the given choices.\newlineThe correct choice that matches the formula an=an1+13a_n = a_{n-1} + 13 is (C) an=an1+13a_n = a_{n-1} + 13.

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