The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Explanation

Let r be the common ratio of the G.P. It is given that the first term is a = 1. Now,
`a_(3)+a_(5)=90`
or `ar^(2)+ar^(4)=90`
or `r^(2)+r^(4)=90`
or `r^(4)+r^(2)-90=0`
or `r^(4)+10r^(2)-9r^(2)-90=0`
or `(r^(2)+10)(r^(2)-9)=0`
or `r^(2)-9=0`
or `r=pm3`