Question:
If second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first term is
(a) 1/4
(b) 1/2
(c) 2
(d) 4
Solution:
(d) 4
$a_{2}=2$
$\therefore a r=2 \quad \ldots \ldots \ldots(\mathrm{i})$
Also, $S_{\infty}=8$
$\Rightarrow \frac{a}{(1-r)}=8$
$\Rightarrow \frac{a}{\left(1-\frac{2}{a}\right)}=8 \quad[\mathrm{U} \sin \mathrm{g}(\mathrm{i})]$
$\Rightarrow a^{2}=8(a-2)$
$\Rightarrow a^{2}-8 a+16=0$
$\Rightarrow(a-4)^{2}=0$
$\Rightarrow a=4$
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