Answer
Th sequence is geometric with a common ratio of $9$.
The first four terms are:
$f_1=9$
$f_2=81$
$f_3=729$
$f_4=6561$
Work Step by Step
Substitute $1, 2, 3,$ and $4$ for $n$ into the given formula:
$f_1=3^{2\cdot 1}=3^2 = 9$
$f_2=3^{2\cdot 2 }=3^4 = 81$
$f_3=3^{2\cdot 3}=3^6 = 729$
$f_4=3^{2\cdot 4}=3^8 = 6561$
To check if the sequence is geometric, find the ratio of each successive pairs:
$\dfrac{a_2}{a_1}=\dfrac{81}{9}=9$
$\dfrac{a_3}{a_2}=\dfrac{729}{81}=9$
$\dfrac{a_4}{a_3}=\dfrac{6561}{729}=9$
The common ratios are the same, so the sequence is geometric with a common ratio of $9$.
