The interior angle of a $'n$' sided convex polygon are in $G.P$.. The smallest angle is $1^o $ and common ratio is $2^o $ then number of possible values of $'n'$ is

Find the sum of the following series up to n terms:

$5+55+555+\ldots$

if $x = \,\frac{4}{3}\, - \,\frac{{4x}}{9}\, + \,\,\frac{{4{x^2}}}{{27}}\, - \,\,.....\,\infty $ , then $x$ is equal to

Let $a_1, a_2, a_3, \ldots$. be a $GP$ of increasing positive numbers. If the product of fourth and sixth terms is $9$ and the sum of fifth and seventh terms is $24 ,$ then $a_1 a_9+a_2 a_4 a_9+a_5+a_7$ is equal to $.........$.

If $a,b,c$ are in $A.P.$, then ${2^{ax + 1}},{2^{bx + 1}},\,{2^{cx + 1}},x \ne 0$ are in

If the sum of $n$ terms of a $G.P.$ is $255$ and ${n^{th}}$ terms is $128$ and common ratio is $2$, then first term will be