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Which recursive formula can be used to define this sequence for n>1n > 1?\newline11,12,13,14,15,16,11, 12, 13, 14, 15, 16, \ldots\newlineChoices:\newline(A) an=1an1a_n = 1a_{n-1}\newline(B) an=1211an1a_n = \frac{12}{11}a_{n-1}\newline(C) an=an11a_n = a_{n-1} - 1\newline(D) an=an1+1a_n = a_{n-1} + 1

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline11,12,13,14,15,16,11, 12, 13, 14, 15, 16, \ldots\newlineChoices:\newline(A) an=1an1a_n = 1a_{n-1}\newline(B) an=1211an1a_n = \frac{12}{11}a_{n-1}\newline(C) an=an11a_n = a_{n-1} - 1\newline(D) an=an1+1a_n = a_{n-1} + 1
  1. Sequence Type: We have the sequence: 11,12,13,14,15,16,11, 12, 13, 14, 15, 16, \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 1111 and 1212.\newline1211=112 - 11 = 1\newlineCommon difference (dd): 11
  3. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSince the common difference is 11, the recursive formula will be of the form an=a(n1)+da_n = a_{(n-1)} + d.\newlineSubstitute 11 for dd in an=a(n1)+da_n = a_{(n-1)} + d.\newlineRecursive formula: an=a(n1)+1a_n = a_{(n-1)} + 1

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