Answer
A recursive rule for the sequence is $a_1=7,a_n=a_{n-1}+9$
Work Step by Step
The given sequence from the table is
$7,16,25,34,...$
The first term is $a_1=7$.
Calculate difference between each pair of consecutive terms.
$16-7=9$
$25-16=9$
$34-25=9$
The common difference is $d=9$.
So, the sequence is arithmetic.
Recursive equation for an arithmetic sequence.
$a_n=a_{n-1}+d$
Substitute $9$ for $d$.
$a_n=a_{n-1}+9$
Hence, a recursive rule for the sequence is $a_1=7,a_n=a_{n-1}+9$
