If sum of infinite terms of a G.P. is 3 and sum of squares of its… - Vidyadip

MCQ

If sum of infinite terms of a $G.P.$ is $3$ and sum of squares of its terms is $3$, then its first term and common ratio are

✓
$3/2, 1/2$
B
$1, 1/2$
C
$3/2, 2$
D
None of these

✓

Answer

Correct option: A.

$3/2, 1/2$

a
(a) $\frac{a}{{1 - r}} = 3$ …..(i)

and $\frac{{{a^2}}}{{1 - {r^2}}} = 3$ .....(ii)

From (i) and (ii), $\frac{a}{{1 + r}} = 1$

$\Rightarrow a = 1 + r$

From (i), $\frac{{1 + r}}{{1 - r}} = 3 $

$\Rightarrow r = \frac{1}{2}$ , from (i), $ a = 3/2$

So, first term $= 3/2$ and common ratio $= 1/2.$

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