jee-main 2020 Q54

jee-main · India · session2_05sep_shift2 Geometric Sequences and Series Finite Geometric Sum and Term Relationships

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:
(1) $\frac{1}{26}\left(3^{49}-1\right)$
(2) $\frac{1}{26}\left(3^{50}-1\right)$
(3) $\frac{2}{13}\left(3^{50}-1\right)$
(4) $\frac{1}{13}\left(3^{50}-1\right)$

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:\\
(1) $\frac{1}{26}\left(3^{49}-1\right)$\\
(2) $\frac{1}{26}\left(3^{50}-1\right)$\\
(3) $\frac{2}{13}\left(3^{50}-1\right)$\\
(4) $\frac{1}{13}\left(3^{50}-1\right)$

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