The sum of a $G.P.$ with common ratio $3$ is $364$, and last term is $243$, then the number of terms is

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

$0.5737373...... = $

If the sum and product of four positive consecutive terms of a $G.P.$, are $126$ and $1296$, respectively, then the sum of common ratios of all such $GPs$ is $.........$.

$0.14189189189….$ can be expressed as a rational number

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