Question

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

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

The correct option is B

$\frac{1}{3}$

Explanation for correct option

Let $a,ar,a{r}^2,....$ be in GP

It is given, every term of the series is twice the previous

$$\begin{gathered} \therefore ar=2a \\ \Rightarrow r=2 \end{gathered}$$

Given that the sum of first two term is $1$

$\begin{array}{rcl}\therefore a+ar& =& 1\\ & \Rightarrow & a\left(1+r\right)=1\\ \Rightarrow a\left(1+2\right)& =& 1\left[\because r=2\right]\\ & \Rightarrow & a=\frac{1}{3}\end{array}$

Hence, option B is correct.