If $S_n$ stands for the sum of $n$ terms of a $GP$ with $a$ as the first term and $r$ as the common ratio,then $S_n : S_{2n}$ is

The sum of some terms of a $G.P.$ is $315$,whose first term and the common ratio are $5$ and $2$ respectively. Find the last term and the number of terms.

In an increasing geometric progression of positive terms,the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4^{\text{th}}$,$6^{\text{th}}$,and $8^{\text{th}}$ terms is:

The first two terms of a geometric progression add up to $12$. The sum of the third and the fourth terms is $48$. If the terms of the geometric progression are alternately positive and negative,then the first term is

If $p, q, r$ are in a geometric progression and $a, b, c$ are in another geometric progression,then $cp, bq, ar$ are in...

Which term of the sequence $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \dots$ is $\frac{1}{19683}$?