Answer
A recursive rule for the sequence is
$a_1=3,a_n=2a_{n-1}$
Work Step by Step
The given sequence is
$3,6,12,24,48,...$
The first term is $a_1=3$.
Calculate ratio between each pair of consecutive terms.
$\frac{6}{3}=2$
$\frac{12}{6}=2$
$\frac{24}{12}=2$
$\frac{48}{24}=2$
The common ratio is $r=2$.
So, the sequence is geometric.
Recursive equation for a geometric sequence.
$a_n=r\cdot a_{n-1}$
Substitute $2$ for $r$.
$a_n=2a_{n-1}$
Hence, a recursive rule for the sequence is $a_1=3,a_n=2a_{n-1}$
