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Which recursive formula can be used to define this sequence for n>1n > 1?\newline15,22,29,36,43,50,15, 22, 29, 36, 43, 50, \ldots\newlineChoices:\newline(A) an=an1+7a_{n} = a_{n-1} + 7\newline(B) an=an1+an17a_{n} = a_{n-1} + a_{n-1} - 7\newline(C) an=2215an1a_{n} = \frac{22}{15}a_{n-1}\newline(D) an=an1+an1+7a_{n} = a_{n-1} + a_{n-1} + 7

Full solution

Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline15,22,29,36,43,50,15, 22, 29, 36, 43, 50, \ldots\newlineChoices:\newline(A) an=an1+7a_{n} = a_{n-1} + 7\newline(B) an=an1+an17a_{n} = a_{n-1} + a_{n-1} - 7\newline(C) an=2215an1a_{n} = \frac{22}{15}a_{n-1}\newline(D) an=an1+an1+7a_{n} = a_{n-1} + a_{n-1} + 7
  1. Sequence Type: We have the sequence: 15,22,29,36,43,50,15, 22, 29, 36, 43, 50, \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: 2215=722 - 15 = 7\newlineCommon difference (dd): 77
  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, where dd is the common difference.\newlineSubstitute 77 for dd in the formula.\newlineRecursive formula: an=an1+7a_n = a_{n-1} + 7
  4. Match with Choices: Match the recursive formula we found with the given choices.\newlineThe correct choice is (A)an=a(n1)+7(A) a_n = a_{(n-1)} + 7.

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