Question:
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:
Correct Option: , 2
Solution:
Let the first term be ' $a$ ' and common ratio be ' $r$ '.
$\because \operatorname{ar}\left(1+r+r^{2}\right)=3$ ...(1)
and $a r^{5}\left(1+r+r^{2}\right)=243$..(2)'
From (1) and (2),
$r^{4}=81 \Rightarrow r=3$ and $a=\frac{1}{13}$
$\therefore S_{50}=\frac{a\left(r^{50}-1\right)}{r-1}=\frac{3^{50}-1}{26} \quad\left[\because S_{n}=\frac{a\left(r^{n}-1\right)}{(r-1)}\right]$