If `S` denotes the sum of an infinite G.P. adn `S_1` denotes the sum of the squares of its terms, then prove that the first term and common ratio are respectively `(2S S_1)/(s^2+S_1)a n d(S^2-S_1)/(S^2+S_1)` .

Explanation

To solve the problem, we need to find the first term \( a \) and the common ratio \( r \) of an infinite geometric progression (G.P.) given the sum \( S \) of the G.P. and the sum \( S_1 \) of the squares of its terms.

### Step-by-Step Solution:

1. **Understanding the Sums**:
The sum \( S \) of an infinite G.P. with first term \( a \) and common ratio \( r \) (where \( |r| < 1 \)) is given by:
\[
S = \frac{a}{1 - r}
...