In an increasing G.P. , the sum of the first and the last term is 66, the product of the second and the last but one is 128 and the sum of the terms is 126. How many terms are there in the progression?

Explanation

To solve the problem step by step, we need to analyze the given conditions of the geometric progression (G.P.) and derive the necessary equations.

### Step 1: Define the Terms of the G.P.
Let the first term of the G.P. be \( a \) and the common ratio be \( r \). The terms of the G.P. can be expressed as:
- First term: \( a \)
- Second term: \( ar \)
- Third term: \( ar^2 \)
- Last term (n-th term): \( ar^{n-1} \)
...