If three numbers are in $G.P.$,then their logarithms will be in

Find the fractional value of $0.125125125 \dots$

$1 - \frac{2}{3} + \frac{2 \cdot 4}{3 \cdot 6} - \frac{2 \cdot 4 \cdot 6}{3 \cdot 6 \cdot 9} + \ldots \infty =$

In a geometric progression with positive terms,if each term is equal to the sum of the next two terms,then the common ratio of the progression is = .......

The sum of the first three terms of a $G.P.$ is $\frac{39}{10}$ and their product is $1$. Find the common ratio and the terms.

If $x, y, z$ are in $G.P.$ and $a^x = b^y = c^z$,then