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Which recursive formula can be used to define this sequence for n>1n > 1?\newline4,11,26,41,56,71,-4, 11, 26, 41, 56, 71, \ldots\newlineChoices:\newline(A)an=an1+15a_{n} = a_{n-1} + 15\newline(B)an=an1+an215a_{n} = a_{n-1} + a_{n-2} - 15\newline(C)an=114an1a_{n} = -\frac{11}{4}a_{n-1}\newline(D)an=115an1a_{n} = \frac{1}{15}a_{n-1}

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline4,11,26,41,56,71,-4, 11, 26, 41, 56, 71, \ldots\newlineChoices:\newline(A)an=an1+15a_{n} = a_{n-1} + 15\newline(B)an=an1+an215a_{n} = a_{n-1} + a_{n-2} - 15\newline(C)an=114an1a_{n} = -\frac{11}{4}a_{n-1}\newline(D)an=115an1a_{n} = \frac{1}{15}a_{n-1}
  1. Sequence Type Determination: We have the sequence: 4,11,26,41,56,71,ext...-4, 11, 26, 41, 56, 71, ext{...}\newlineIs the given sequence geometric or arithmetic?\newlineThe difference between consecutive terms appears to be constant.\newlineThe given sequence is likely arithmetic.
  2. Calculation of Differences: To confirm that the sequence is arithmetic, we calculate the difference between consecutive terms.\newlineDifference between the first and second term: 11(4)=1511 - (-4) = 15\newlineDifference between the second and third term: 2611=1526 - 11 = 15\newlineSince the difference is the same, the sequence is indeed arithmetic with a common difference of 1515.
  3. Recursive Formula Identification: Identify the recursive formula for the given arithmetic sequence.\newlineThe common difference is 1515, so the recursive formula will involve adding 1515 to the previous term.\newlineThe correct recursive formula is: an=a(n1)+15a_n = a_{(n-1)} + 15
  4. Matching with Choices: Now, we match our recursive formula with the given choices.\newlineThe correct choice that represents the recursive formula an=an1+15a_n = a_{n-1} + 15 is:\newline(A) a=a+15a = a + 15

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