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Which recursive formula can be used to define this sequence for n>1n > 1?\newline1,4,7,10,13,16,1, 4, 7, 10, 13, 16, \ldots\newlineChoices:\newline(A) an=an13a_n = a_{n-1} - 3\newline(B) an=an1+an13a_n = a_{n-1} + a_{n-1} - 3\newline(C) an=4an1a_n = 4a_{n-1}\newline(D) an=an1+3a_n = a_{n-1} + 3

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline1,4,7,10,13,16,1, 4, 7, 10, 13, 16, \ldots\newlineChoices:\newline(A) an=an13a_n = a_{n-1} - 3\newline(B) an=an1+an13a_n = a_{n-1} + a_{n-1} - 3\newline(C) an=4an1a_n = 4a_{n-1}\newline(D) an=an1+3a_n = a_{n-1} + 3
  1. Sequence Type: We have the sequence: 1,4,7,10,13,16,1, 4, 7, 10, 13, 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. Two consecutive terms are 11 and 44. 41=34 - 1 = 3 Common difference (dd) is 33.
  3. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSince the sequence is arithmetic with a common difference of 33, the recursive formula will involve adding 33 to the previous term.\newlineThe correct recursive formula is: an=an1+3a_n = a_{n-1} + 3

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