Question

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.

Answer 1

Let a and r be the first term and the common ratio of the G.P. respectively.

∴ a = 1

a₃ = ar² = r²

a₅ = ar⁴ = r⁴

∴ r² + r⁴ = 90

⇒ r⁴ + r² – 90 = 0

Thus, the common ratio of the G.P. is ±3.