Sum of first n terms of an AP (having positive terms) is given by $S_{n} = (1 + 2 T_{n}) (1 - T_{n})$ (where $T_{n}$
is the $n^{t h}$ term of the series ). Then the value of $2 {T_{1}}^{2}$ is

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$2$

$4$

$1$

$6$

answer is C.

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Detailed Solution

We have for $n = 1, S_{1} = T_{1}$
$\Rightarrow T_{1} = (1 + 2 T_{1}) (1 - T_{1}) \Rightarrow T_{1} = \frac{1}{\sqrt{2}} \Rightarrow 2 {T_{1}}^{2} = 1$

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