If $s$ is the sum of an infinite $G.P.$, the first term $a$ then the common ratio $r$ given by

Find the sum up to $20$ terms in the geometric progression $0.15,0.015,0.0015........$

The value of $0.\mathop {234}\limits^{\,\,\, \bullet \,\, \bullet } $ is

The value of ${a^{{{\log }_b}x}}$, where $a = 0.2,\;b = \sqrt 5 ,\;x = \frac{1}{4} + \frac{1}{8} + \frac{1}{{16}} + .........$to $\infty $ is

Let $a _1, a _2, a _3, \ldots$ be a $G.P.$ of increasing positive numbers. Let the sum of its $6^{\text {th }}$ and $8^{\text {th }}$ terms be $2$ and the product of its $3^{\text {rd }}$ and $5^{\text {th }}$ terms be $\frac{1}{9}$. Then $6\left( a _2+\right.$ $\left.a_4\right)\left(a_4+a_6\right)$ is equal to

Fifth term of a $G.P.$ is $2$, then the product of its $9$ terms is