If $a, b, c$ are in $G.P.$,then

In an increasing geometric progression of positive terms,the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the third and fifth terms is $49$. Then the sum of the $4^{\text{th}}$,$6^{\text{th}}$,and $8^{\text{th}}$ terms is:

Find the sum of the first $9$ terms of the geometric series $1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \dots$

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 $S_1 + S_3 + S_5 + \dots + S_{2n-1}$?

If $G$ is the geometric mean of $x$ and $y$,then $\frac{1}{G^2 - x^2} + \frac{1}{G^2 - y^2} = $

If $\alpha, \beta$ are the roots of the equation $x^2 - 3x + a = 0$ and $\gamma, \delta$ are the roots of the equation $x^2 - 12x + b = 0$,and if $\alpha, \beta, \gamma, \delta$ form an increasing $G.P.$,then $(a, b) = $