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8. Sequences and Series
medium
If $2^{10}+2^{9} \cdot 3^{1}+28 \cdot 3^{2}+\ldots+2 \cdot 3^{9}+3^{10}=S -211$ then $S$ is equal to
A
$\frac{3^{11}}{2}+2^{10}$
B
$3^{11}-2^{12}$
C
$3^{11}$
D
$2 \cdot 3^{11}$
(JEE MAIN-2020)
Solution
$a =2^{10} ; r =\frac{3}{2} ; n =11( G \cdot P )$
$S^{\prime}=\left(2^{10}\right) \frac{\left(\left(\frac{3}{2}\right)^{11}-1\right)}{\frac{3}{2}-1}=2^{11}\left(\frac{3^{11}}{2^{11}}-1\right)$
$S^{\prime}=3^{11}-2^{11}= S -2^{11}( Given )$
$\therefore S =3^{11}$
Standard 11
Mathematics
