Question

In a gp tn-2:tn-5=1:8 then the common ratio is?

Answer 1

Common ratio is `1/2`

Explanation:

Let the first term in GP be `a` and common ratio be `r`, then `n^(th)` term is given by `t_n=ar^(n-1)`

Hence `t_(n-2)=ar^(n-2-1)=ar^(n-3)` and

`t_(n-5)=ar^(n-5-1)=ar^(n-6)`

as `t_(n-2):t_(n-5)=1:8`

i.e. `(ar^(n-3))/(ar^(n-6))=1/8`

or `r^(n-3-(n-6))=1/8`

or `r^(n-3-n+6)=1/8` i.e. `r^3=1/8`

and hence `r=root(3)(1/8)=1/2`

i.e. common ratio is `1/2`