Question

In the first term of gp is 1 the sum of third and fifth term is 90 find common ratio gp

Answer 1

Let a, ar, ar^2, ar^3, ar^4.... are in GP.

Given a= 1, r is common ratio.

Then third term is r^2 and 5th term is r^4 & their sum is 90.

Hence, r^4 + r^2 = 90

r^4 + r^2 - 90 = 0

Solving this, we get

r^2= - 10 (or) +9

r^2 = 9

r = +3 or -3 (r is common ratio)

Third term is r^2 = +9 (even if r = 3 or -3)

Fifth term is r^4 = +81,

Hence, Gp is

1, 3, 9, 27, 81,... (When r= 3)

and 1, -3, 9, -27, 81,.... (When r= --3)