The $G.M.$ of the numbers $3, 3^2, 3^3, ..., 3^n$ is

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 $6(a_2 + a_4)(a_4 + a_6)$ is equal to

If the sum of three terms of a Geometric Progression $(GP)$ is $19$ and their product is $216$, then which of the following is a possible common ratio of this $GP$?

If the sum of three terms of a $G.P.$ is $19$ and their product is $216$,then the common ratio of the series is

For a sequence $(t_{n})$,if $s_{n} = 7(3^{n} - 1)$,then $t_{n} =$

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