Question

Given the following geometric sequence, find the common ratio:

{225, 45, 9...}

Answer 1

`r=(1)/(5)`

Explanation:

We are given that a geometric sequence

225,45,9,...

We have to find the common ratio of the geometric sequence.

`a=225,a_2=45,a_3=9`

`r=(a_2)/(a_1)`

`a_2=ar`

Substitute the values then we get

`45=225r`

`r=(45)/(225)`

`r=(1)/(5)`

Hence, the common ratio of the geometric sequence =
`(1)/(5)`

Answer 2

`(1)/(5)` is the common ratio

Explanation:

Common ratio(r) states that the ratio of each term of a geometric sequence to the term preceding it.

`r = (a_2)/(a_1) =(a_3)/(a_2)........(a_(n+1))/(a_n)`

Given the sequence:

225, 45, 9, .........

Here,

`a_1 = 225`

`a_2 = 45`

`a_3 = 9` and so on...

Using definition to find r.

`r = (45)/(225)=(9)/(45)......`

After solving we get;

`r = (1)/(5)`

Therefore, the common ratio is,
`(1)/(5)`