Question

If second term of a G.P is 2 and its sum to infinity is 8.Find its first term

Answer 1

General term $r$th term of

G.P$=a{r}^{n-1}$

$\Rightarrow$ $ar=2$

Infinite sum $=\frac{a}{1-r}=8$

$\Rightarrow$ $a=8-8r$

$\Rightarrow$ $\frac{2}{r}=8-8r$

$\Rightarrow$ $2=8r-8r^2$

$\Rightarrow$ $4r^2-4rH=0$

$\Rightarrow$ $4r^2-2r-2rH=0$

$\Rightarrow$ ${(2r-1)}^2=0$

$\Rightarrow$ $r=\frac{1}{2}$

$\Rightarrow$ $a=8-4=4$