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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=an1+an23a_n = a_{n-1} + a_{n-2} - 3\newline(B)an=an13a_n = 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=an1+an23a_n = a_{n-1} + a_{n-2} - 3\newline(B)an=an13a_n = 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.\newlineTwo consecutive terms are 11 and 44.\newline41=34 - 1 = 3\newlineCommon difference (dd): 33
  3. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSince the common difference is 33, the recursive formula will add 33 to the previous term.\newlineRecursive formula: an=a(n1)+3a_n = a_{(n-1)} + 3
  4. Match with Choices: Match the recursive formula with the given choices.\newlineThe correct choice that matches an=an1+3a_n = a_{n-1} + 3 is:\newline(D) an=an1+3a_n = a_{n-1} + 3

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