# If the sum of the second , 3rd, 4th terms of a positive term GP is 3 & the sum of 6th , 7th & 8th terms is 243 then the sum of first 50 terms of GP is  Option: 1 Option: 2 Option: 3 Option: 4

$\\a x+a r^{2}+a b^{3}=3 \\ a x^{5}+a r^{6}+a b^{7}=243 \\ h^{4}=81 \Rightarrow n=3$

$\\a(3+4+27)=3 \\ \Rightarrow a=\frac{1}{12}$

\begin{aligned} \therefore S_{50}&= \frac{a\left(r^{50}-1\right)}{(r-1)} \\ &=\frac{1}{13}\left(\frac{3^{50}-1}{2}\right) \end{aligned}

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