The sum of some terms of a geometric progression is $728$. If the common ratio is $3$ and the last term is $486$,what is the first term of the progression?

If the fifth term of a $G.P.$ is $2$,then the product of its first $9$ terms is:

If the sum of the first $6$ terms is $9$ times the sum of the first $3$ terms of the same $G.P.$,then the common ratio of the series will be

The least positive integer $n$ such that $1 - \frac{2}{3} - \frac{2}{3^2} - \dots - \frac{2}{3^{n-1}} < \frac{1}{100}$ is

If $r > 1$,$x = a + \frac{a}{r} + \frac{a}{r^2} + \dots \infty$,$y = b - \frac{b}{r} + \frac{b}{r^2} - \dots \infty$,and $z = c + \frac{c}{r^2} + \frac{c}{r^4} + \dots \infty$,then $\frac{xy}{z} = \dots$

If $2^{10} + 2^{9} \cdot 3^{1} + 2^{8} \cdot 3^{2} + \ldots + 2^{1} \cdot 3^{9} + 3^{10} = S - 2^{11}$,then $S$ is equal to