Question

If $2^{10}+2^9\cdot 3^1+2^8\cdot 3^2+\dots +2\cdot 3^9+3^{10}=S-2^{11}$ then $S$ is equal to :

• A. $\frac{3^{11}}{2}+2^{10}$
• B. $3^{11}-2^{12}$
• C. $3^{11}$
• D. $2\cdot 3^{11}$

Answer 1

Answer: (C)

$a=2^{10};r=\frac{3}{2};n=11$ (G.P.)
$S^{\prime }=\left(2^{10}\right)\frac{\left({\left(\frac{3}{2}\right)}^{11}-1\right)}{\frac{3}{2}-1}=2^{11}\left(\frac{3^{11}}{2^{11}}-1\right)$
$S^{\prime }=3^{11}-2^{11}=S-2^{11}$ (Given )
$\therefore S=3^{11}$