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.

Answer

N/a

Explanation

Let r be the common ratio of the given G.P.
`because` First term a = 1, so third term `a_(3) = ar^(2) = 1 * r^(2) = r^(2)`
and 5th term `a_(5) = ar^(4) = 1 * r^(4) = r^(4)`
Sum of 3rd and 5th terms `= r^(2) + r^(4) = 90`
`rArr` `r^(4) + r^(2) = 90`
`rArr` `r^(4) + r^(2) - 90 = 0`
`rArr` `r^(4) + 10r^(2) - 9r^(2) - 90 = 0`
`rArr` `(r^(2) - 9)(r^(2) + 10) = 0`
`rArr` `r^(2) = 9 or - 10`
`rArr` `r = +-3 or sqrt(-10)`
But `sqrt(-10)` is an imaginary number which is not acceptable for r.
Therefore, common ratio `r = +- 3`