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

Let $A_{1}, A_{2}, A_{3}, \ldots$ 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

Find the sum to the indicated number of terms in the geometric progression: $x^{3}, x^{5}, x^{7}, \ldots$ for $n$ terms (where $x \neq \pm 1$).

If $S_n$ is the sum of $n$ terms of a geometric progression with first term $a$ and common ratio $r$,what is the sum of $S_1 + S_3 + S_5 + \dots + S_{2n-1}$?

Write the first five terms of the sequence whose $n^{th}$ term is $a_{n} = 2^{n}$.

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 $G.P.s$ is $.........$.