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

Divide $155$ into three parts such that the three numbers are in a Geometric Progression $(GP)$ and the first term is $120$ less than the third term.

If the arithmetic mean and geometric mean of the $p^{\text{th}}$ and $q^{\text{th}}$ terms of the sequence $-16, 8, -4, 2, \ldots$ satisfy the equation $4x^{2}-9x+5=0$,then $p+q$ is equal to ..... .

Let $a_1, a_2, ..., a_{10}$ be a $G.P.$ If $\frac{a_3}{a_1} = 25$,then $\frac{a_9}{a_5}$ is equal to:

If the sum of an infinite $G.P.$ and the sum of the squares of its terms is $3$,then the common ratio of the first series is

Find a $G.P.$ for which the sum of the first two terms is $-4$ and the fifth term is $4$ times the third term.