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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! :)

User CuongHuyTo
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1 Answer

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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.
User Hgascon
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