ANSWER
[tex]a_n= \frac{2}{5} ( {5}^{n - 1} )[/tex]
EXPLANATION
The recursive rule for the geometric sequence is
[tex]a_1=\frac{2}{5} ;a_n=5a_{n-1}[/tex]
This implies that:
The common ratio is;
[tex]r = 5[/tex]
The explicit rule is given by:
[tex]a_n=a_1( {r}^{n - 1} )[/tex]
We substitute the values to obtain;
[tex]a_n= \frac{2}{5} ( {5}^{n - 1} )[/tex]
