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?

Let $a, b, c$ be positive integers such that $\frac{b}{a}$ is an integer. If $a, b, c$ are in geometric progression and the arithmetic mean of $a, b, c$ is $b+2$,then the value of $\frac{a^2+a-14}{a+1}$ is

If $n$ geometric means are inserted between $a$ and $b$,then the $n^{th}$ geometric mean will be:

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

Find the sum of the first $n$ terms and the sum of the first $5$ terms of the geometric series $1 + \frac{2}{3} + \frac{4}{9} + \dots$

The product of three consecutive terms of a geometric progression is $216$ and the sum of the products of these terms taken two at a time is $156$. Find the terms.