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

Let the G.P. is ,

`a,ar,ar^2,...oo`

Here, `a` is the first term and `r` is the common ratio of the G.P.

Then,

`S = a/(1-r) => a = S(1-r)`

Now, second G.P. will be,

`a^2,a^2r^2,a^2r^4...oo`

Then,`S_1 = a^2/(1-r^2)`

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