Answer :
Given,
The sequence is 6, 9, 13.5, 20.25,...
Required
The recursive formula of the sequence.
Here,
First term is 6.
The common ratio between the consecutive terms is,
[tex]\begin{gathered} \frac{9}{6}=1.5 \\ \frac{13.5}{9}=1.5 \\ \frac{20.25}{13.5}=1.5 \end{gathered}[/tex]So, the recursive formula for the sequence is,
[tex]\begin{gathered} a_n=ar^{n-1} \\ Here,\text{ a = 6, and r = 1.5} \\ a_n=6(1.5)^{n-1} \end{gathered}[/tex]Hence, the recursive formula is 6(1.5)^(n-1).