Answer
An explicit rule for the sequence is
$ a_n=17n-13$
Work Step by Step
The given recursive rule is
$a_1=4,a_n=a_{n-1}+17$
First term is $a_1=4$.
and common difference $d=17$.
Explicit rule for an arithmetic sequence.
$\Rightarrow a_n=a_1+(n-1)d$
Substitute $4$ for $a_1$ and $17$ for $d$.
$\Rightarrow a_n=4+(n-1)17$
Use distributive property.
$\Rightarrow a_n=4+17n-17$
Simplify.
$\Rightarrow a_n=17n-13$