Find the first four terms of the sequence defined below, where [tex]$n$[/tex] represents the position of a term in the sequence. Start with [tex]$n=1$[/tex].

[tex]f(n) = 3(3)^n[/tex]

1. [tex]f(1) = \square[/tex]
2. [tex]f(2) = \square[/tex]
3. [tex]f(3) = \square[/tex]
4. [tex]f(4) = \square[/tex]



Answer :

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].