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  4. The geometric series a + ar + ar 2+ ar 3+ ldots ldots . ∞ has a sum of 7 and the terms involving odd powers of r has a sum of 3. The value of (a+r) equals

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Q. The geometric series $a + ar + ar ^2+ ar ^3+\ldots \ldots . \infty$ has a sum of 7 and the terms involving odd powers of $r$ has a sum of 3. The value of $(a+r)$ equals

Sequences and Series

Solution:

$\frac{ a }{1- r }=7$....(1)
and $\frac{ ar }{1- r ^2}=3$ ......(2)
solving $r =3 / 4$ and $a =7 / 4 $
$\Rightarrow a + r =5 / 2$