Answer
A recursive rule for the sequence is $a_1=3,a_n=a_{n-1}+5$
Work Step by Step
The given sequence is
$3,8,13,18,23,...$
The first term is $a_1=3$.
Calculate difference between each pair of consecutive terms.
$8-3=5$
$13-8=5$
$18-13=5$
$23-18=5$
The common difference is $d=5$.
So, the sequence is arithmetic.
Recursive equation for an arithmetic sequence.
$a_n=a_{n-1}+d$
Substitute $5$ for $d$.
$a_n=a_{n-1}+5$
Hence, a recursive rule for the sequence is $a_1=3,a_n=a_{n-1}+5$