Question

Given the following geometric sequence, find the common ratio: {225, 45, 9, ...}.

Answer 1

The common ratio is 1/5

Answer 2

Answer: The required common ratio for the given geometric sequence is
`(1)/(5).`

Step-by-step explanation: We are given to find the common ratio for the following geometric sequence :

225, 45, 9, . . .

We know that

in a geometric sequence, the ratio of any term with the preceding term is the common ratio of the sequence.

For the given geometric sequence, we have

a(1) = 225, a(2) = 45, a(3) = 9, etc.

So, the common ratio (r) is given by

`r=(a(2))/(a(1))=(a(3))/(a(2))=~~.~~.~~.~~.`

We have

`(a(2))/(a(1))=(45)/(225)=(1)/(5),\\\\\\(a(3))/(a(2))=(9)/(45)=(1)/(5),~etc.`

Therefore, we get

`r=(1)/(5).`

Thus, the required common ratio for the given geometric sequence is
`(1)/(5).`