Question

Find the common ratio and the general term of the following geometric sequences.
$\frac{2}{5},\frac{6}{25},\frac{18}{125},....$

Answer 1

Given sequence is a geometric sequence.
The common ratio is given by $r=\frac{t_2}{t_1}=\frac{t_3}{t_2}=.....$
Thus, $r=\frac{\frac{6}{25}}{\frac{2}{5}}=\frac{3}{5}$.
The first term of the sequence is $\frac{2}{5}$.

So, the general term of the sequence is
$t_n=a{r}^{n-1},n=1,2,3,....$
$\Rightarrow t_n=\frac{2}{5}{\left(\frac{3}{5}\right)}^{n-1},n=1,2,3,.....$