Question

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

a) 1
b) 2
c) 3
d) 4​

Answer 1

The answer would be C.

Answer 2

C

Explanation:

The n th term formula of a geometric sequence is

`a_(n)` = a
`r^(n-1)`

where a is the first term and r the common ratio

Using the second and fourth term, then

ar = 6 → (1)

ar³ = 54 → (2)

Divide (2) by (1)

`(ar^3)/(ar)` =
`(54)/(6)` = 9

r² = 9 ⇒ r =
`√(9)` = 3 → C