For a sequence,a_1 = 2 and frac{a_{n+1}}{a_n} | vedclass

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(B) The given sequence is a Geometric Progression $(G.P.)$ with the first term $a = 2$ and common ratio $r = \frac{1}{3}$.
The sum of the first $n$ t

Vedclass · Accepted Answer

$3\left(1 - \frac{1}{3^{20}}\right)$

Vedclass · Answer

(B) The given sequence is a Geometric Progression $(G.P.)$ with the first term $a = 2$ and common ratio $r = \frac{1}{3}$.
The sum of the first $n$ terms of a $G.P.$ is given by $S_n = \frac{a(1 - r^n)}{1 - r}$.
For $n = 20$,$S_{20} = \frac{2 \left(1 - (\frac{1}{3})^{20}ight)}{1 - \frac{1}{3}}$.
$S_{20} = \frac{2 \left(1 - \frac{1}{3^{20}}ight)}{\frac{2}{3}}$.
$S_{20} = 2 	imes \frac{3}{2} \left(1 - \frac{1}{3^{20}}ight) = 3 \left(1 - \frac{1}{3^{20}}ight)$.

For a sequence,$a_1 = 2$ and $\frac{a_{n+1}}{a_n} = \frac{1}{3}$. Then $\sum_{r=1}^{20} a_r$ is

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