JEE PYQ: Sequence And Series Question 29
Question 29 - 2020 (05 Sep Shift 1)
If $2^{10} + 2^9 \cdot 3^1 + 2^8 \cdot 3^2 + \ldots + 2 \times 3^9 + 3^{10} = S - 2^{11}$ then $S$ is equal to:
(1) $3^{11} - 2^{12}$
(2) $3^{11}$
(3) $\frac{3^{11}}{2} + 2^{10}$
(4) $2 \cdot 3^{11}$
Show Answer
Answer: (2)
Solution
Given sequence are in G.P. and common ratio $\frac{3}{2}$
$\therefore \frac{2^{10}\left(\left(\frac{3}{2}\right)^{11} - 1\right)}{\frac{3}{2} - 1} = S - 2^{11}$
$\Rightarrow \frac{2^{10}\left(\frac{3^{11} - 2^{11}}{2^{11}}\right)}{\frac{1}{2}} = S - 2^{11}$
$\Rightarrow 3^{11} - 2^{11} = S - 2^{11} \Rightarrow S = 3^{11}$
BETA
