JEE PYQ: Sequence And Series Question 31
Question 31 - 2020 (05 Sep Shift 2)
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) $\frac{1}{26}(3^{49} - 1)$
(2) $\frac{1}{26}(3^{50} - 1)$
(3) $\frac{2}{13}(3^{50} - 1)$
(4) $\frac{1}{13}(3^{50} - 1)$
Show Answer
Answer: (2)
Solution
Let first term be ‘$a$’ and common ratio be ‘$r$’.
$\therefore ar(1 + r + r^2) = 3$ …(1)
and $ar^5(1 + r + r^2) = 243$ …(2)
From (1) and (2),
$r^4 = 81 \Rightarrow r = 3$ and $a = \frac{1}{13}$
$\therefore S_{50} = \frac{a(r^{50} - 1)}{r - 1} = \frac{3^{50} - 1}{26}$
BETA
