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Which recursive formula can be used to define this sequence for n>1n > 1?\newline15,28,41,54,67,80,15, 28, 41, 54, 67, 80, \ldots\newlineChoices:\newline(A)an=an1+13a_{n} = a_{n-1} + 13\newline(B)an=113an1a_{n} = \frac{1}{13}a_{n-1}\newline(C)an=2714an1a_{n} = \frac{27}{14}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?\newline15,28,41,54,67,80,15, 28, 41, 54, 67, 80, \ldots\newlineChoices:\newline(A)an=an1+13a_{n} = a_{n-1} + 13\newline(B)an=113an1a_{n} = \frac{1}{13}a_{n-1}\newline(C)an=2714an1a_{n} = \frac{27}{14}a_{n-1}\newline(D)an=an1+an113a_{n} = a_{n-1} + a_{n-1} - 13
  1. Sequence Type: We have the sequence: 15,28,41,54,67,80,15, 28, 41, 54, 67, 80, \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: 2815=1328 - 15 = 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 Formula 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:\newline(A) a=a+13a = a + 13\newlineHowever, this choice is not correctly written. It should be an=an1+13a_n = a_{n-1} + 13, not a=a+13a = a + 13.

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