To find the first four terms of the sequence defined by the function [tex]\( f(n) = 3 \cdot 3^n \)[/tex], we will calculate the values of [tex]\( f(n) \)[/tex] for [tex]\( n = 1, 2, 3, \)[/tex] and [tex]\( 4 \)[/tex].
1. For the first term of the sequence, where [tex]\( n = 1 \)[/tex]:
[tex]\[
f(1) = 3 \cdot 3^1 = 3 \cdot 3 = 9
\][/tex]
2. For the second term of the sequence, where [tex]\( n = 2 \)[/tex]:
[tex]\[
f(2) = 3 \cdot 3^2 = 3 \cdot 9 = 27
\][/tex]
3. For the third term of the sequence, where [tex]\( n = 3 \)[/tex]:
[tex]\[
f(3) = 3 \cdot 3^3 = 3 \cdot 27 = 81
\][/tex]
4. For the fourth term of the sequence, where [tex]\( n = 4 \)[/tex]:
[tex]\[
f(4) = 3 \cdot 3^4 = 3 \cdot 81 = 243
\][/tex]
Thus, the first four terms of the sequence are [tex]\( 9 \)[/tex], [tex]\( 27 \)[/tex], [tex]\( 81 \)[/tex], and [tex]\( 243 \)[/tex].
