Question

A recursive rule for a geometric sequence is a1=8;an=3/4(an-1). What is the explicit rule for this sequence?

A. an = 1/4 (8)n-1

B. an=8(3/4)n-1

C. an =3/4 (8)n-1

Answer 1

B. an=8(3/4)^(n-1)

Explanation:

The general term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

The recursive rule for the sequence tells you the first term is 8 and the common ratio is 3/4. Then the explicit rule is ...

an = 8(3/4)^(n-1) . . . . . matches choice B