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

Answer: (B)

$\frac{1}{3}$

Answer 2

We have, common ratio r = 2; $\left\lbrack \because\frac{a_{n}}{a_{n - 1}} = 2 \right\rbrack$

Let a be the first term, then $a + ar = 1$

⇒$a(1 + r) = 1$ ⇒ $a = \frac{1}{1 + r} = \frac{1}{1 + 2} = \frac{1}{3}$