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

If the first term of a $G.P.$ $a_1, a_2, a_3, \dots$ is unity such that $4a_2 + 5a_3$ is least,then the common ratio of the $G.P.$ is

What is the geometric mean of the observations $2, 4, 8, 16, 32, 64$?

The $4^{th}$ term of a $G.P.$ is the square of its second term,and the first term is $-3$. Determine its $7^{th}$ term.

Let ${a_n}$ be the ${n^{th}}$ term of a $G$.$P$. of positive numbers. Let $\sum\limits_{n = 1}^{100} {{a_{2n}}} = \alpha$ and $\sum\limits_{n = 1}^{100} {{a_{2n - 1}}} = \beta$,such that $\alpha \ne \beta$,then the common ratio is

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