The sequence given is a geometric sequence.
A geometric sequence has the explicit formula in the form:
[tex]\begin{gathered} u(n)=ar^{n-1} \\ where \\ a=first\text{ }term \\ r=common\text{ }ratio \end{gathered}[/tex]
and the recursive formula in the form:
[tex]u(n+1)=u(n)\times r[/tex]
The question provides the following parameters:
[tex]a=u(1)=16[/tex]
The recursive formula is given to be:
[tex]u(n+1)=9u(n)[/tex]
Therefore, the common ratio is:
[tex]r=9[/tex]
Hence, the explicit formula is given to be:
[tex]u(n)=16(9)^{n-1}[/tex]
OPTION B is correct.
