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So I have learned to program using recursion, but I have not learned how to actually do this in math. If I have the sequence {4,8,12}, and the question asks for a recursive formula to solve for an+1, would it be as simple as: an+1 = an + 4 ? This seems correct to me, but it also seems too simple.

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1 Answer

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If the explicit formula for a sequence is $a_n=a_1+n(d-1)$, then the recursive formula is $a_n=a_{n-1}+d$. Here, we have that the explicit formula is $a_n=4+4(n-1)$, then the recursive formula will be $a_n=a_{n-1}+4$. You are correct.

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