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Which recursive formula can be used to define this sequence for n>1n > 1?\newline5,19,33,47,61,75,5, 19, 33, 47, 61, 75, \ldots\newlineChoices:\newline(A) an=an1+an214a_n = a_{n-1} + a_{n-2} - 14\newline(B) an=an1+14a_n = a_{n-1} + 14\newline(C) an=14an1a_n = 14a_{n-1}\newline(D) an=195an1a_n = \frac{19}{5}a_{n-1}

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline5,19,33,47,61,75,5, 19, 33, 47, 61, 75, \ldots\newlineChoices:\newline(A) an=an1+an214a_n = a_{n-1} + a_{n-2} - 14\newline(B) an=an1+14a_n = a_{n-1} + 14\newline(C) an=14an1a_n = 14a_{n-1}\newline(D) an=195an1a_n = \frac{19}{5}a_{n-1}
  1. Identify Sequence Type: We have the sequence: 5,19,33,47,61,75,5, 19, 33, 47, 61, 75, \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: 195=1419 - 5 = 14.\newlineCommon difference (dd): 1414.
  3. Identify 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 1414 for dd in the formula.\newlineRecursive formula: an=an1+14a_n = a_{n-1} + 14.
  4. Match with Choices: Match the recursive formula with the given choices.\newlineThe correct formula is (B)an=a(n1)+14(B) a_n = a_{(n-1)} + 14.

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