Answer
A recursive rule for the sequence is
$a_1=2,a_n=a_{n-1}+1.5$
Work Step by Step
The given sequence is
$2,3.5,5,6.5,...$
The first term is $a_1=2$.
Calculate difference between each pair of consecutive terms.
$3.5-2=1.5$
$5-3.5=1.5$
$6.5-5=1.5$
The common difference is $d=1.5$.
So, the sequence is arithmetic.
Recursive equation for an arithmetic sequence.
$a_n=a_{n-1}+d$
Substitute $1.5$ for $d$.
$a_n=a_{n-1}+1.5$
Hence, a recursive rule for the sequence is $a_1=2,a_n=a_{n-1}+1.5$
