Question

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! :)

Answer 1

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.