The first term of a GP is 1 and the sum of its 3rd and 5th terms is 90. Find the common ratio of the GP.

Explanation

To solve the problem step by step, let's denote the first term of the geometric progression (GP) as \( a \) and the common ratio as \( r \).

### Step 1: Identify the first term and express the terms of the GP
The first term \( a \) is given as 1. Therefore, we can express the terms of the GP as follows:
- First term: \( a = 1 \)
- Second term: \( ar = 1 \cdot r = r \)
- Third term: \( ar^2 = 1 \cdot r^2 = r^2 \)
- Fourth term: \( ar^3 = 1 \cdot r^3 = r^3 \)
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