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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=an1+an24a_n = a_{n-1} + a_{n-2} - 4\newline(B) an=an1+4a_n = a_{n-1} + 4\newline(C) an=4an1a_n = 4a_{n-1}\newline(D) an=139an1a_n = \frac{13}{9}a_{n-1}

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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=an1+an24a_n = a_{n-1} + a_{n-2} - 4\newline(B) an=an1+4a_n = a_{n-1} + 4\newline(C) an=4an1a_n = 4a_{n-1}\newline(D) an=139an1a_n = \frac{13}{9}a_{n-1}
  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, by subtracting any term from the term that follows it.\newlineFor example, take the first two terms: 1313 and 99.\newline139=413 - 9 = 4\newlineCommon difference (dd): 44
  3. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSince the common difference is 44, the recursive formula will involve adding 44 to the previous term.\newlineThe correct recursive formula is: an=a(n1)+4a_n = a_{(n-1)} + 4
  4. Match with Choices: Match the correct recursive formula with the given choices.\newlineThe correct formula, an=an1+4a_n = a_{n-1} + 4, corresponds to choice (B)(B).

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