The sum to infinity of the progression $9 - 3 + 1 - \frac{1}{3} + .....$ is

$2.\mathop {357}\limits^{ \bullet \,\, \bullet \,\, \bullet } = $

Which term of the following sequences:

$\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots$ is $\frac{1}{19683} ?$

Let ${a_n}$ be the ${n^{th}}$ term of the G.P. of positive numbers. Let $\sum\limits_{n = 1}^{100} {{a_{2n}}} = \alpha $ and $\sum\limits_{n = 1}^{100} {{a_{2n - 1}}} = \beta $, such that $\alpha \ne \beta $,then the common ratio is

Find the $12^{\text {th }}$ term of a $G.P.$ whose $8^{\text {th }}$ term is $192$ and the common ratio is $2$

The difference between the fourth term and the first term of a Geometrical Progresssion is $52.$ If the sum of its first three terms is $26,$ then the sum of the first six terms of the progression is