The sum of the first three terms of an increasing G.P. is 21 and the sum of their squares is 189. Then the sum of its first n terms is

Options

A. `3(2^(n) -1)`
B. `12(1 - (1)/(2^(n)))`
C. `6(1 - (1)/(2^(n)))`
D. `6 (2^(n) -1)`

Answer

To solve the problem step by step, we will start by defining the terms of the increasing geometric progression (G.P.) and then use the given conditions to derive the required sum of the first n terms.

### Step 1: Define the terms of the G.P.
Let the first three terms of the increasing G.P. be:
- First term = \( a \)
- Second term = \( ar \)
- Third term = \( ar^2 \)