Question

In a geometric sequence, a2=2, a3=16, and a4=128.

Which equation can be used to find the nth term of the sequence, an?


an=8⋅2n−1

an=2n−1

an=14⋅8n−1

an=2⋅14n−1

Answer 1

an = 1/4(8)^n-1

Explanation:

Given the following in a geometric sequence, a2=2, a3=16, and a4=128.

nth term of a sequence = ar^n-1

a is the first term

r is the common ratio

r = a3/a2 = a4/a3

r = 16/2 = 128/16

r = 8

a2 = ar

2 = 8a

a = 2/8

a = 1/4

The nth term by substituting the parameters will be;

an = 1/4(8)^n-1