Answer
A recursive rule for the sequence is $a_1=4,a_n=5a_{n-1}$
Work Step by Step
The given sequence is
$4,20,100,500,2500,...$
The first term is $a_1=4$.
Calculate ratio between each pair of consecutive terms.
$\frac{20}{4}=5$
$\frac{100}{20}=5$
$\frac{500}{100}=5$
$\frac{2500}{500}=5$
The common ratio is $d=5$.
So, the sequence is geometric.
Recursive equation for a geometric sequence.
$a_n=r\cdot a_{n-1}$
Substitute $5$ for $r$.
$a_n=5a_{n-1}$
Hence, a recursive rule for the sequence is $a_1=4,a_n=5a_{n-1}$
