Question

Find the sum to infinity of the G.P.: $5,\frac{20}{7},\frac{80}{49},...$

Answer 1

The sequence is a decreasing G.P. as the common ratio $\left(r\right)$ is less than one. Common ratio in a G.P. is given by the second term divided by the first term.

Here,

First term $a=5$

So, $r=\frac{\frac{20}{7}}{5}$

$r=\frac{4}{7}$

The sum $\left(S\right)$ of the infinite terms of a G.P. is given by $S=\frac{a}{1-r}$ where $r<1.$

$S=\frac{5}{1-\frac{4}{7}}$

$\Rightarrow S=\frac{35}{3}$