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

Explanation

Let the common ratio of the G.P. be r
Here , first term = a = 1
`rArr ar^(2) + ar^(4) = 90 `
`rArr r^(4) + r^(2) - 90 = 0 " "[because a = 1] `
`rArr (r^(2) + 10 ) (r^(2) - 9 ) = 0 `
`rArr r^(2) = 9 " "[because t^(2) ne - 10 ]`
`rArr = pm 3 `
` therefore ` The common ratio of the G.P. is 3 or - 3 .