The sum of a few terms of a geometric series is $728$. If the common ratio is $3$ and the last term is $486$,then the first term of the series will be:

If in a $G.P.$ of $64$ terms,the sum of all the terms is $7$ times the sum of the odd terms of the $G.P.$,then the common ratio of the $G.P.$ is equal to

In a $G.P.$, if the product of the first three terms is $27$ and the set of all possible values for the sum of its first three terms is $\mathbb{R} - (a, b)$, then $a^{2} + b^{2}$ is equal to . . . . . . .

If the sum of the second,fourth and sixth terms of a $G.P.$ of positive terms is $21$ and the sum of its eighth,tenth and twelfth terms is $15309$,then the sum of its first nine terms is:

If $\frac{6}{3^{12}} + \frac{10}{3^{11}} + \frac{20}{3^{10}} + \frac{40}{3^{9}} + \dots + \frac{10240}{3} = 2^{n} \cdot m$,where $m$ is odd,then $m \cdot n$ is equal to

The sum of $100$ terms of the series $0.9 + 0.09 + 0.009 + \dots$ will be