Answer
A recursive rule for the sequence is $a_1=8,a_n=a_{n-1}-5$.
Work Step by Step
The given sequence is
$8,3,-2,-7,-12,...$
The first term is $a_1=8$.
Calculate difference between each pair of consecutive terms.
$3-8=-5$
$-2-3=-5$
$-7-(-2)=-7+2=-5$
$-12-(-7)=-12+7=-5$
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 $a_1=8,a_n=a_{n-1}-5$.
