The sum of the first two terms of a GP is 1 and every term of this series is twice of its previous term, then the first term will be

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The sum of the first two terms of a GP is 1 and every term of this series is twice of its previous term, then the first term will be

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$\frac{3}{4}$

$\frac{2}{3}$

$\frac{1}{4}$

$\frac{1}{3}$

answer is B.

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Detailed Solution

Given, $a_{1} + a_{2} = 1$

and $a_{n} = 2 \cdot a_{n - 1}, n \geq 2$

Let a be the first term and $r$ be the common ratio, then

$a + a r = 1$ (i) and $a r = 2 a [∵ a_{2} = 2 a_{1}]$

$\Rightarrow r = 2$ (ii)

From Eqs. (i) and (ii),

$\begin{array}{l} \Rightarrow 3 a = 1 \\ a = \frac{1}{3} \end{array}$

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