Answer
A recursive rule for the sequence is
$a_1=35,a_n=a_{n-1}-11$
Work Step by Step
The given sequence from the graph is
$35,24,13,2,...$
The first term is $a_1=35$.
Calculate difference between each pair of consecutive terms.
$24-35=-11$
$13-24=-11$
$2-13=-11$
The common difference is $d=-11$.
So, the sequence is arithmetic.
Recursive equation for an arithmetic sequence.
$a_n=a_{n-1}+d$
Substitute $-11$ for $d$.
$a_n=a_{n-1}-11$
Hence, a recursive rule for the sequence is $a_1=35,a_n=a_{n-1}-11$
