The first term of a GP is 1. The sum of the 3rd and 5th terms of 90. Then the common ratio is
2
Let the common ratio be r.
The first term = 1
The second term = 1*r = r
The third term = r*r = r^2
The fourth term = r^2*r = r^3
The fifth term = r^3*r = r^4
The sum of the 3rd and 5th terms is given as 90:
r^2 + r^4 = 90
r^2(1 + r^2) = 90
r^2(1 + r)(1 - r) = 90
Since the first term is 1, r cannot be negative. So, (1 - r) = 1
r = 1
Therefore, the common ratio is 2.