For a sequence < a_n > , ; a_1 = 2 and a_ n + 1 a_n = 1 3 . Then … - Vidyadip

MCQ

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

A
$\frac{{20}}{2}[4 + 19 \times 3]$
✓
$3\left( {1 - \frac{1}{{{3^{20}}}}} \right)$
C
$2(1 - {3^{20}})$
D
None of these

✓

Answer

Correct option: B.

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

b
(b) The sequence is a $G.P.$ with common ratio $\frac{1}{3}$.

Now from $\frac{{a(1 - {r^n})}}{{1 - r}},\,\,\,\,\frac{{2\,[1 - {{(1/3)}^{20}}]}}{{1 - (1/3)}}$ = $3\,\left[ {1 - \frac{1}{{{3^{20}}}}} \right]$.

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