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Which recursive formula can be used to define this sequence for n > 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=2215an1a_{n} = \frac{22}{15}a_{n-1}\newline(C) an=an1+an17a_{n} = a_{n-1} + a_{n-1} - 7\newline(D) an=an1+an1+7a_{n} = a_{n-1} + a_{n-1} + 7

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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=2215an1a_{n} = \frac{22}{15}a_{n-1}\newline(C) an=an1+an17a_{n} = a_{n-1} + a_{n-1} - 7\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. Calculate Differences: To confirm that the sequence is arithmetic, we calculate the difference between consecutive terms.\newlineThe difference between the first two terms is 2215=722 - 15 = 7.\newlineThe difference between the second and third terms is 2922=729 - 22 = 7.\newlineSince the difference is the same, the sequence is indeed arithmetic with a common difference of 77.
  3. Identify Recursive Formula: Now, we need to identify the recursive formula for the given arithmetic sequence.\newlineThe recursive formula for an arithmetic sequence is generally an=an1+da_n = a_{n-1} + d, where dd is the common difference.\newlineIn this case, d=7d = 7.\newlineTherefore, the recursive formula is an=an1+7a_n = a_{n-1} + 7.
  4. Match with Choices: We match our recursive formula with the given choices.\newlineThe correct choice that represents the recursive formula an=an1+7a_n = a_{n-1} + 7 is:\newline(A) a=a+7a = a + 7\newlineHowever, this choice is not correctly written. It should be an=an1+7a_n = a_{n-1} + 7, not just a=a+7a = a + 7.

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