Question

Enter the explicit rule for the sequence

Answer 1

ANSWER

$a_n= \frac{2}{5} ( {5}^{n - 1} )$

EXPLANATION

The recursive rule for the geometric sequence is

$a_1=\frac{2}{5} ;a_n=5a_{n-1}$

This implies that:

The common ratio is;

$r = 5$

The explicit rule is given by:

$a_n=a_1( {r}^{n - 1} )$

We substitute the values to obtain;

$a_n= \frac{2}{5} ( {5}^{n - 1} )$