12)
Given data:
The given series is 5, 15, 45, 135, 405...
The geometric ratio is,
[tex]\begin{gathered} r=\frac{15}{5} \\ =3 \end{gathered}[/tex]
The expression for recursive rule is,
[tex]\begin{gathered} a_n=a_{n-1}(r)^{} \\ =a_{n-1}(3) \end{gathered}[/tex]
The expression for the explicit formula is,
[tex]\begin{gathered} a_n=ar^{n-1} \\ =5(3)^{n-1} \end{gathered}[/tex]
Thus, the recursive rule is an-1(3), and explicit rule is 5(3)^(n-1).
