Question

The sum of first two terms of a G.P is $\frac{5}{3}$ and the sum to infinite terms is 3. What is the first term?

• A. 1
• B. 6
• C. 9
• D.

Answer 1

The correct option is A 1

The first two terms = a, ar

$a+ar=\frac{5}{3}$

$\frac{a}{(1-r)}=3$

$a=3(1-r)$

$a(1+r)=\frac{5}{3}$

$3(1-r)(1+r)=\frac{5}{3}$

$1-r^2=\frac{5}{9}$

$r^2=\frac{4}{9}$

$r=\frac{2}{3}$

$a=3(1-\frac{2}{3})=1$

First term is 1.