If the $(m + n)^{th}$ term of a geometric progression is $9$ and the $(m - n)^{th}$ term is $4$,what is the $m^{th}$ term?

The sum of a few terms of a geometric series is $728$. If the common ratio is $3$ and the last term is $486$,then the first term of the series will be:

If in a $G.P.$ of $64$ terms,the sum of all the terms is $7$ times the sum of the odd terms of the $G.P.$,then the common ratio of the $G.P.$ is equal to

The sum of the first ten terms of a geometric progression is $S_1$ and the sum of the next ten terms ($11^{th}$ to $20^{th}$) is $S_2$. What is the common ratio?

The sum of an infinite geometric series with positive terms is $3$ and the sum of the cubes of its terms is $\frac{27}{19}$. Then the common ratio of this series is

Find the sum of the products of the corresponding terms of the sequences $2, 4, 8, 16, 32$ and $128, 32, 8, 2, \frac{1}{2}$.