The first term of a $G.P.$ whose second term is $2$ and sum to infinity is $8$, will be
$6$
$3$
$4$
$1$
If $S$ is the sum to infinity of a $G.P.$, whose first term is $a$, then the sum of the first $n$ terms is
Let $A _{1}, A _{2}, A _{3}, \ldots \ldots$ be an increasing geometric progression of positive real numbers. If $A _{1} A _{3} A _{5} A _{7}=\frac{1}{1296}$ and $A _{2}+ A _{4}=\frac{7}{36}$, then, the value of $A _{6}+ A _{8}+ A _{10}$ is equal to
The sum of a $G.P.$ with common ratio $3$ is $364$, and last term is $243$, then the number of terms is
The remainder when the polynomial $1+x^2+x^4+x^6+\ldots+x^{22}$ is divided by $1+x+x^2+x^3+\ldots+x^{11}$ is
The G.M. of the numbers $3,\,{3^2},\,{3^3},\,......,\,{3^n}$ is