Find the $10^{\text{th}}$ and $n^{\text{th}}$ terms of the $G.P.$ $5, 25, 125, \ldots$

Find the fractional value of $0.125125125 \dots$

If the roots of $x^3-k x^2+14 x-8=0$ are in geometric progression,then $k$ is equal to

If $\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}$ and $x \neq 0$,then $a, b, c, d$ are in

If $\frac{6}{3^{12}} + \frac{10}{3^{11}} + \frac{20}{3^{10}} + \frac{40}{3^{9}} + \dots + \frac{10240}{3} = 2^{n} \cdot m$,where $m$ is odd,then $m \cdot n$ is equal to

The sum of the first two terms of a geometric progression is $12$. The sum of the third and fourth terms is $48$. The terms of the geometric progression alternate between positive and negative. What is the first term?