The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$, will be

Let $a _1, a _2, a _3, \ldots$ be a $G.P.$ of increasing positive numbers. Let the sum of its $6^{\text {th }}$ and $8^{\text {th }}$ terms be $2$ and the product of its $3^{\text {rd }}$ and $5^{\text {th }}$ terms be $\frac{1}{9}$. Then $6\left( a _2+\right.$ $\left.a_4\right)\left(a_4+a_6\right)$ is equal to

A $G.P.$ consists of an even number of terms. If the sum of all the terms is $5$ times the sum of the terms occupying odd places, then the common ratio will be equal to

If the sum of the second, third and fourth terms of a positive term $G.P.$ is $3$ and the sum of its sixth, seventh and eighth terms is $243,$ then the sum of the first $50$ terms of this $G.P.$ is

If the sum of $n$ terms of a $G.P.$ is $255$ and ${n^{th}}$ terms is $128$ and common ratio is $2$, then first term will be

The $6^{th}$ term of a $G.P.$ is $32$ and its $8^{th}$ term is $128$, then the common ratio of the $G.P.$ is