Answer: Option C
[tex]a_n=3(6)^{n-1}[/tex]
Step-by-step explanation:
The number of rabbits in each generation can be modeled using a geometric sequence of the form:
[tex]a_n=a_1(r)^{n-1}[/tex]
Where [tex]a_1[/tex] is the first term of the sequence, [tex]a_n[/tex] is the ninth term of the series, r is the common ratio
To find the proportion we divide the consecutive terms of the sequence as shown
[tex]\frac{18}{3}=6\\\\\frac{108}{18}=6[/tex]
Then the common ratio is: [tex]r=6[/tex]
The first term of the series is: [tex]a_1=3[/tex]
Then the explicit formula is:
[tex]a_n=3(6)^{n-1}[/tex]
The answer is: Option C
