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Which recursive formula can be used to define this sequence for n>1n > 1?\newline2,6,10,14,18,22,2, 6, 10, 14, 18, 22, \ldots\newlineChoices:\newline(A) an=an1+4a_n = a_{n-1} + 4\newline(B) an=an1+an1+4a_n = a_{n-1} + a_{n-1} + 4\newline(C) an=73an1a_n = \frac{7}{3}a_{n-1}\newline(D) an=an14a_n = a_{n-1} - 4

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Q. Which recursive formula can be used to define this sequence for n>1n > 1?\newline2,6,10,14,18,22,2, 6, 10, 14, 18, 22, \ldots\newlineChoices:\newline(A) an=an1+4a_n = a_{n-1} + 4\newline(B) an=an1+an1+4a_n = a_{n-1} + a_{n-1} + 4\newline(C) an=73an1a_n = \frac{7}{3}a_{n-1}\newline(D) an=an14a_n = a_{n-1} - 4
  1. Sequence Type: We have the sequence: 2,6,10,14,18,22,2, 6, 10, 14, 18, 22, \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 22 and 66.\newline62=46 - 2 = 4\newlineCommon difference (dd): 44
  3. Recursive Formula: Identify the recursive formula for the given sequence.\newlineSubstitute 44 for dd in an=a(n1)+da_n = a_{(n-1)} + d.\newlineRecursive formula: an=a(n1)+4a_n = a_{(n-1)} + 4

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