Question

The sum of first two terms of a GP is $\frac{14}{5}$ and the sum of infinite terms is $\frac{10}{3}$. The first term of the GP if the common ratio is positive is___.

Answer 1

Let a and r be the first term and common ratio respectively.
Given, a + ar=$\frac{14}{5}$ ......(1)
and $\frac{a}{(1-r)}=\frac{10}{3}$
a=$\frac{10(1-r)}{3}$ .......(2)
Substituting (2) in (1),
$\frac{10(1-r^2)}{3}=\frac{14}{5}$
r²=$\frac{4}{25}$
r=$\frac{2}{5}$ (since r is positive)
From (2), a=2
Therefore, first term = a = 2