Geometric series a + ar + ar^2 + ar^3 +..... ∞ has sum 7 and terms involving odd&n

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8. Sequences and Series

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The geometric series $a + ar + ar^2 + ar^3 +..... \infty$ has sum $7$ and the terms involving odd powers of $r$ has sum $'3'$, then the value of $(a^2 -r^2)$ is -

A

$\frac{5}{4}$

B

$\frac{5}{2}$

C

$\frac{25}{4}$

D

$5$

Solution

$\frac{a}{1-r}=7 \quad \ldots(1) \quad \frac{\mathbf{a r}}{1-r^{2}}=3 \quad \ldots(2)$

from $(1)$ and $ (2) \Rightarrow a=\frac{7}{4}$ and $r=\frac{3}{4}$

Standard 11

Mathematics

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