The sum of an infinite geometric series is `15` and the sum of the squares of these terms is `45`. Find the series.

Explanation

Given,


`S_(o o)=(a)/(1-r)=15`


Squaring both sides,


`(a^2)/((1-r)^2)=225``\ \ \ (1)`


Sum of square of terms in G.P.


`(a^2)/((1-r)(1+r))=45``\ \ \ (2)`


Dividing `(1)` by `(2)`


`(1+r)/(1-r)=5`


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