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Which recursive formula can be used to define this sequence for n>1n > 1?\newline4,1,6,11,16,21,-4, 1, 6, 11, 16, 21, \ldots\newlineChoices:\newline(A)an=an1+5a_{n} = a_{n-1} + 5\newline(B)an=15an1a_{n} = \frac{1}{5}a_{n-1}\newline(C)an=an1+an1+5a_{n} = a_{n-1} + a_{n-1} + 5\newline(D)an=11an1a_{n} = 11a_{n-1}

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline4,1,6,11,16,21,-4, 1, 6, 11, 16, 21, \ldots\newlineChoices:\newline(A)an=an1+5a_{n} = a_{n-1} + 5\newline(B)an=15an1a_{n} = \frac{1}{5}a_{n-1}\newline(C)an=an1+an1+5a_{n} = a_{n-1} + a_{n-1} + 5\newline(D)an=11an1a_{n} = 11a_{n-1}
  1. Identify Sequence Type: We have the sequence: 4,1,6,11,16,21,-4, 1, 6, 11, 16, 21, \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 4-4 and 11. 1(4)=51 - (-4) = 5 Common difference (dd): 55
  3. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSubstitute 55 for dd in an=an1+da_n = a_{n-1} + d.\newlineRecursive formula: an=an1+5a_n = a_{n-1} + 5
  4. Match with Choices: Match the recursive formula with the given choices.\newlineThe correct choice is (A)an=a(n1)+5(A) a_n = a_{(n-1)} + 5.

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