Answer
The sequence is geometric with a common ratio of $9$.
Work Step by Step
We need to substitute $1, 2, 3,$ and $4$ for $n$ into the given equation to find the first four terms.
$f_1=3^{2\cdot 1}=3^2 = 9 \\ f_2=3^{2\cdot 2 }=3^4 = 81 \\ f_3=3^{2\cdot 3}=3^6 = 729 \\ f_4=3^{2\cdot 4}=3^8 = 6561$
Our aim is to check if the sequence is geometric and then compute the ratio of each successive pairs.
$\dfrac{a_2}{a_1}=\dfrac{81}{9}=9 \\ \dfrac{a_3}{a_2}=\dfrac{729}{81}=9 \\ \dfrac{a_4}{a_3}=\dfrac{6561}{729}=9$
We can see that the common ratios are the same; thus the sequence is geometric with a common ratio of $9$.
