Answer
A recursive rule for the sequence is $a_1=3,a_n=a_{n-1}+8$
Work Step by Step
The given sequence from the table is
$3,11,19,27,35,...$
The first term is $a_1=3$.
Calculate difference between each pair of consecutive terms.
$11-3=8$
$19-11=8$
$27-19=8$
$35-27=8$
The common difference is $d=8$.
So, the sequence is arithmetic.
Recursive equation for an arithmetic sequence.
$a_n=a_{n-1}+d$
Substitute $8$ for $d$.
$a_n=a_{n-1}+8$
Hence, a recursive rule for the sequence is $a_1=3,a_n=a_{n-1}+8$