Question

Which formula can be used to find the nth term of a geometric sequence where the fifth term is 1/6 and the common ratio is 1/4?

Answer 1

`a_n = 16((1)/(4))^(n - 1)`

Explanation:

Given:

Fifth term of a geometric sequence =
`(1)/(16)`

Common ratio (r) = ¼

Required:

Formula for the nth term of the geometric sequence

Solution:

Step 1: find the first term of the sequence

Formula for nth term of a geometric sequence =
`ar^(n - 1)`, where:

a = first term

r = common ratio = ¼

Thus, we are given the 5th term to be ¹/16, so n here = 5.

Input all these values into the formula to find a, the first term.

`(1)/(16) = a*(1)/(4)^(5 - 1)`

`(1)/(16) = a*(1)/(4)^(4)`

`(1)/(16) = a*(1)/(256)`

`(1)/(16) = (a)/(256)`

Cross multiply

`1*256 = a*16`

Divide both sides by 16

`(256)/(16) = (16a)/(16)`

`16 = a`

`a = 16`

Step 2: input the value of a and r to find the nth term formula of the sequence

nth term =
`ar^(n - 1)`

nth term =
`16*(1)/(4)^(n - 1)`

`a_n = 16((1)/(4))^(n - 1)`