The product $(32)(32)^{1/6}(32)^{1/36} ...... to\,\, \infty $ is

If $a,\;b,\;c$ are in $A.P.$, then ${10^{ax + 10}},\;{10^{bx + 10}},\;{10^{cx + 10}}$ will be in

${7^{th}}$ term of the sequence $\sqrt 2 ,\;\sqrt {10} ,\;5\sqrt 2 ,\;.......$ is

The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \ldots .$ to $\infty$ is equal to

Let the first term $a$ and the common ratio $r$ of a geometric progression be positive integers. If the sum of its squares of first three terms is $33033$, then the sum of these three terms is equal to

Suppose the sides of a triangle form a geometric progression with common ratio $r$. Then, $r$ lies in the interval