Question:
The sum of an infinite geometric series is 6. If its first term is 2, find its common ratio.
Solution:
Given: $\frac{a}{1-r}=6, a=2$
To find: $r=$ ?
$\therefore \frac{2}{1-r}=6$
$\Rightarrow 1-r=\frac{2}{6}=\frac{1}{3}$
$\Rightarrow 3(1-r)=1$
$\Rightarrow 3-3 r=1$
$\Rightarrow 3 r=3-1$
$\Rightarrow r=\frac{2}{3}$
Common ratio $r=\frac{2}{3}$
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