Question

The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3. What is the common ratio in this sequence?

Answer 1

the common ratio in this sequence is 6:2 or 4:3

Answer 2

The common ratio is
`r=\pm(1)/(3)`.

Explanation:

Given : The second term in a geometric sequence is 12. The fourth term in the same sequence is 4/3.

To find : What is the common ratio in this sequence?

Solution :

The nth term of G.P is
`a_n=ar^(n-1)`

The second term in a geometric sequence is 12.

i.e.
`a_2=ar^(2-1)`

`12=ar` .....(1)

The four term in a geometric sequence is
`(4)/(3)`.

i.e.
`a_4=ar^(4-1)`

`(4)/(3)=ar^3` .....(2)

Divide (1) and (2),

`((4)/(3))/(12)=(ar^3)/(ar)`

`(1)/(9)=r^2`

`\sqrt{(1)/(9)}=r`

`\pm(1)/(3)=r`

Therefore, the common ratio is
`r=\pm(1)/(3)`.