Question

What is the common ratio for the geometric sequence?

18,12,8,163,…

Answer 1

`(2)/(3)` is the common ratio.

Explanation:

We have been given the geometric sequence

`18,12,8,(16)/(3)`

We need to find the common ratio:

`\text{common ratio}=(a_2)/(a_1)`

Common ratio is the the ratio which is same between the consecutive numbers

Between 18 and 12
`a_2=12,a_1=18` on substituting the values in the formula we get:

`\text{common ratio}=(12)/(18)=(2)/(3)`

Between 12 and 8
`a_2=8,a_1=12` on substituting the values in the formula we get:

`\text{common ratio}=(8)/(12)=(2)/(3)`

Hence, we will get
`(2)/(3)` as common ratio.