Question

Find the common ratio of the GP whose first and last terms are $25$ and $\frac{1}{625}$ respectively and the sum of the GP is $\frac{19531}{625}$.

Answer 1

We know that the sum of a GP is $\frac{Ter{m}_1-r\left(Ter{m}_{last}\right)}{1-r}$

Therefore,

$\frac{19531}{625}=\frac{25-\left(\frac{r}{625}\right)}{1-r}$

$r=\frac{1}{5}$