If second term of a G.P. is 2 and the sum of its infinite terms is 8,
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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