Answer
A recursive rule for the sequence is
$a_1=8,a_n=3a_{n-1}$
Work Step by Step
The given sequence from the table is
$8,24,72,216,...$
The first term is $a_1=8$.
Calculate ratio between each pair of consecutive terms.
$\frac{24}{8}=3$
$\frac{72}{24}=3$
$\frac{216}{72}=3$
The common ratio is $d=3$.
So, the sequence is geometric.
Recursive equation for a geometric sequence.
$a_n=r\cdot a_{n-1}$
Substitute $3$ for $r$.
$a_n=3a_{n-1}$
Hence, a recursive rule for the sequence is $a_1=8,a_n=3a_{n-1}$
