If $y = x + x^2 + x^3 + \dots \infty$,then $x = $

The third term of a $G$.$P$. is $9$. The product of its first five terms is

In a geometric progression,if the ratio of the sum of the first $5$ terms to the sum of their reciprocals is $49$,and the sum of the first and the third term is $35$,then the first term of this geometric progression is:

The sum of the first two terms of a $G.P.$ is $1$ and every term of this series is twice its previous term. Then,the first term will be:

If $S_n$ is the sum of $n$ terms of a geometric progression with first term $a$ and common ratio $r$,what is the sum of $S_1 + S_3 + S_5 + \dots + S_{2n-1}$?

If the sum of an infinite geometric series is $3$ and the sum of the squares of its terms is also $3$,what are the first term and the common ratio of the series?