Question

A geometric sequence is defined by the explicit formula an = 5(-4)n-1. What is the recursive formula for the nth term of this sequence?

A. an = -5an-1
B. an+1 = 4an
C. an+1 = 5an
D. an = -4an-1

Answer 1

an = 5(-4)^(n - 1)
an + 1 = 5(-4)^(n + 1 - 1) = 5(-4)^n
an = 5(-4)^(n - 1) = 5(-4)^n/(-4) = an + 1/(-4)
an + 1 = -4an
an + 1 - 1 = -4 an - 1
an = -4an - 1