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

$\frac{a}{r}, \, a, \, ar$ 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,.......
$\therefore \, \, S_{\infty}=\frac{4}{1 - r}=8$