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Which recursive formula can be used to define this sequence for n>1n > 1?\newline9,13,17,21,25,29,9, 13, 17, 21, 25, 29, \ldots\newlineChoices:\newline(A) an=4an1a_n = 4a_{n-1}\newline(B) an=139an1a_n = \frac{13}{9}a_{n-1}\newline(C) an=an1+an24a_n = a_{n-1} + a_{n-2} - 4\newline(D) an=an1+4a_n = a_{n-1} + 4

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline9,13,17,21,25,29,9, 13, 17, 21, 25, 29, \ldots\newlineChoices:\newline(A) an=4an1a_n = 4a_{n-1}\newline(B) an=139an1a_n = \frac{13}{9}a_{n-1}\newline(C) an=an1+an24a_n = a_{n-1} + a_{n-2} - 4\newline(D) an=an1+4a_n = a_{n-1} + 4
  1. Sequence Type: We have the sequence: 9,13,17,21,25,29,9, 13, 17, 21, 25, 29, \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.\newlineTwo consecutive terms are 99 and 1313.\newline139=413 - 9 = 4\newlineCommon difference (dd): 44
  3. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSince the sequence is arithmetic with a common difference of 44, the recursive formula will add this common difference to the previous term.\newlineRecursive formula: an=an1+4a_n = a_{n-1} + 4

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