For what values of $x$ are the numbers $\frac{2}{7}, x, \frac{7}{2}$ in $G.P.$?

The sum of the first two terms of a $G.P.$ is $1$ and every term of this series is twice its previous term. Then,the first term will be:

The first and last terms of a $G.P.$ are $a$ and $l$ respectively; $r$ being its common ratio; then the number of terms in this $G.P.$ is

Find the sum to the indicated number of terms in the geometric progression: $1, -a, a^{2}, -a^{3}, \ldots$ to $n$ terms (if $a \neq -1$).

If in a geometric progression $\{a_n\}$,$a_1 = 3$,$a_n = 96$ and $S_n = 189$,then the value of $n$ is

The arithmetic mean of two numbers $b$ and $c$ is $a$,and $g_1$ and $g_2$ are two geometric means between them. If $g_1^3 + g_2^3 = kabc$,then $k = \dots$