For a sequence < {aₙ} > ,{a₁} = 2 and frac{{{a_{n + 1}}}}{{{aₙ}}} = frac{1}{3} . Then Σ

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8. Sequences and Series

easy

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

$\frac{{20}}{2}[4 + 19 \times 3]$

B

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

C

$2(1 - {3^{20}})$

D

None of these

Solution

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

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

Standard 11

Mathematics

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