Question

The sum of infinite decreasing GP, such that the sum of whose first three terms is equal to $7$ and the product of the same three terms is $8$ , is equal to

Answer 1

Answer: 8

$\frac{a}{r},a,ar$ are three number
$=a^3=8=a=2$
$2\left(\frac{1}{r}+1+r\right)=7=2r^2-5r+2=0$
$=r=\frac{1}{2}or2$
$\therefore =\frac{1}{2}\left(\therefore r<1\right)$
Thus number are 4, 2, 1,.......
$\therefore S_{\infty }=\frac{4}{1-r}=8$