Answer
A recursive rule for the sequence is
$a_1=0,a_n=a_{n-1}-3$
Work Step by Step
The given sequence from the table is
$0,-3,-6,-9,-12,...$
The first term is $a_1=0$.
Calculate difference between each pair of consecutive terms.
$-3-0=-3$
$-6-(-3)=-6+3=-3$
$-9-(-6)=-9+6=-3$
$-12-(-9)=-12+9=-3$
The common difference is $d=-3$.
So, the sequence is arithmetic.
Recursive equation for an arithmetic sequence.
$a_n=a_{n-1}+d$
Substitute $8$ for $d$.
$a_n=a_{n-1}-3$
Hence, a recursive rule for the sequence is $a_1=0,a_n=a_{n-1}-3$
