Question

What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54, respectively?

A. 1
B. 2
C. 3
D. 4

Answer 1

C

Explanation:

For a geometric sequence the n th term is

`a_(n)` =
`a_(1)`
`r^(n-1)`, hence

`a_(2)` =
`a_(1)` r = 6 → (1)

`a_(4)` =
`a_(1)`
`r^(3)` = 54 → (2)

divide (2) by (1) cancelling
`a_(1)`, hence

`(r^(3) )/(r)` =
`(54)/(6)`

hence
`r^(2)` = 9 ( take the square root of both sides )

r = 3 → C