If n^{th} term of geometric progression 5, - frac{5}{2},frac{5}{4}, - frac{5}{8},... is frac{5}{{102

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8. Sequences and Series

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If the $n^{th}$ term of geometric progression $5, - \frac{5}{2},\frac{5}{4}, - \frac{5}{8},...$ is $\frac{5}{{1024}}$, then the value of $n$ is

A

$11$

B

$10$

C

$9$

D

$4$

Solution

(a)$T_n = ar^{n-1}$

$⇒ {5 \over {1024}}=5({-1 \over 2})^{n-1}$

==> ${\left( {\frac{{ – 1}}{2}} \right)^{10}} = {\left( {\frac{{ – 1}}{2}} \right)^{n – 1}}$

==> $10 = n – 1$

==> $n = 11$.

Standard 11

Mathematics

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