Question

If the sum of the infinity of the series $3+5r+7r^2+$.... is $\frac{44}{9}$, then find the value of r.

Answer 1

Sum of an infinite geometric progression (G.P.)

$S_n=\frac{a}{1-r}$ where $(|r|<1)$

series: $3+5r+7r^2+....$

$S_n=\frac{44}{9}$ & $a=3$

$\therefore \frac{3}{1-r}=\frac{44}{9}$

$1-r=\frac{3\times 9}{44}=\frac{27}{44}$

$r=1-\frac{27}{44}=\frac{17}{44}$

The value of r will be $17/44$.