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8. Sequences and Series
medium
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
A
$3/2, 1/2$
B
$1, 1/2$
C
$3/2, 2$
D
None of these
Solution
(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 $= 1/2.$
Standard 11
Mathematics
