If the sum of the second, third and fourth terms of a positive term $G.P.$ is $3$ and the sum of its sixth, seventh and eighth terms is $243,$ then the sum of the first $50$ terms of this $G.P.$ is
$\frac{2}{13}\left(3^{50}-1\right)$
$\frac{1}{26}\left(3^{50}-1\right)$
$\frac{1}{13}\left(3^{50}-1\right)$
$\frac{1}{26}\left(3^{49}-1\right)$
The sum of the series $5.05 + 1.212 + 0.29088 + ...\,\infty $ is
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
The roots of the equation
$x^5 - 40x^4 + px^3 + qx^2 + rx + s = 0$ are in $G.P.$ The sum of their reciprocals is $10$. Then the value of $\left| s \right|$ is
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
Find the sum of $n$ terms in the geometric progression $\sqrt{7}, \sqrt{21}, 3 \sqrt{7}, \ldots$