Question

A Geometric Sequence has 3rd term of 12 and 5th term of 48. What are the possible values for the common ratio?

Answer 1

`+-2`

Explanation:

Suppose the first term of the GP is `a`, and the common ratio is `r`, then the GP sequence would be :

`{a, ar, ar^2, ar^3, ..., ar^(n-1) }`

We are given that:

`3^(rd) " term" = 12 => ar^2=12` ..... [A]
`5^(th) " term" = 48 => ar^4=48` ..... [B]

Eq [B] `divide` Eq [A]:

`(ar^4)/(ar^2)=48/12`
`:. r^2=4`
`:. r=+-2`