Question

If $2^{10}+2^{9} \cdot 3^{1}+2^{8} \cdot 3^{2}+\ldots+2 \cdot 3^{9}+3^{10}= S -2^{11}$ 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 )
$\therefore S =3^{11}$