Answer
A recursive rule for the sequence is $a_1=1.3,a_n=a_{n-1}+1.3$
Work Step by Step
The given sequence is
$1.3,2.6,3.9,5.2,6.5,...$
The first term is $a_1=1.3$.
Calculate difference between each pair of consecutive terms.
$2.6-1.3=1.3$
$3.9-2.6=1.3$
$5.2-3.9=1.3$
$6.5-5.2=1.3$
The common difference is $d=1.3$.
So, the sequence is arithmetic.
Recursive equation for an arithmetic sequence.
$a_n=a_{n-1}+d$
Substitute $1.3$ for $d$.
$a_n=a_{n-1}+1.3$
Hence, a recursive rule for the sequence is $a_1=1.3,a_n=a_{n-1}+1.3$
