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Multiple Choice!! Find the next two terms in the sequence –5, 8, –13, 20, –29, …. Write a formula for the nth term. Identify the formula as explicit or recursive.

A)40, –53; an = (–1)n • (an – 1 + 2n – 1); explicit

B)39, –50; an = (–1)n • (an – 1 + 2n – 1); explicit

C)40, –53; an = (–1)n • (n2 + 4); recursive

D)none of these

Thanks for your help! :)

Verified Answer :

LammettHash

If \(a_n=(-1)^n(a_{n-1}+2n-1)\), then \(a_6=(-1)^6(-29+2(6)-1)=-18\), so neither (A) nor (B) are correct. Besides, these formulas are recursive, not explicit.

If \(a_n=(-1)^n(n^2+4)\), then the next term is \(a_6=(-1)^6(6^2+4)=40\), and the term after that is \(a_7=(-1)^7(7^2+4)=-53\). However, this sequence is explicit, not recursive, so C is also incorrect.

So the answer is D.

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