Question

The first term of an infinite G.P. exceeds the second term by $2$ and the sum of G.P. is $50$. Then sum of the values of first term is equal to

Answer 1

$a-ar=2\Rightarrow a=\frac{2}{1-r}$

$\frac{a}{1-r}=50\Rightarrow \frac{2}{{\left(1-r\right)}^2}=50$

${\left(1-r\right)}^2=\frac{2}{50}=\frac{1}{25}$

$1-r=\pm \frac{1}{5}$ $r=\frac{4}{5},\frac{6}{5}$

$a=\frac{2}{1-\frac{4}{5}}=10$

$a=\frac{2}{1-\frac{5}{5}}=-10$

Sum of the values of first term is equal to $0$