If three numbers are in $G.P.$,then their logarithms will be in

Let $a_{n}$ be the $n^{\text{th}}$ term of a $G$.$P$. of positive terms. If $\sum_{n=1}^{100} a_{2n+1} = 200$ and $\sum_{n=1}^{100} a_{2n} = 100$,then $\sum_{n=1}^{200} a_{n}$ is equal to:

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

Suppose the sides of a triangle form a geometric progression with common ratio $r$. Then,$r$ lies in the interval

If the $n^{th}$ term of the geometric progression $5, - \frac{5}{2}, \frac{5}{4}, - \frac{5}{8}, \dots$ is $\frac{5}{1024}$,then the value of $n$ is:

Find the $20^{\text{th}}$ and $n^{\text{th}}$ terms of the $G.P.$ $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, \dots$