The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the GP.

Explanation

To solve the problem, we need to find the first term (a), the common ratio (r), and the sum to n terms of a geometric progression (G.P.) given the following conditions:

1. The sum of the first three terms is 16.
2. The sum of the next three terms is 128.

### Step-by-Step Solution:

**Step 1: Set up the equations for the sums.**
...