To find the first five terms of the sequence defined by the function [tex]\( f(n) = n^2 - 2n - 4 \)[/tex], we will calculate the value of [tex]\( f(n) \)[/tex] for each of the first five integers starting from [tex]\( n = 1 \)[/tex].
1. First term ([tex]\( n = 1 \)[/tex]):
[tex]\[
f(1) = 1^2 - 2 \cdot 1 - 4 = 1 - 2 - 4 = -5
\][/tex]
So, the first term is [tex]\( -5 \)[/tex].
2. Second term ([tex]\( n = 2 \)[/tex]):
[tex]\[
f(2) = 2^2 - 2 \cdot 2 - 4 = 4 - 4 - 4 = -4
\][/tex]
So, the second term is [tex]\( -4 \)[/tex].
3. Third term ([tex]\( n = 3 \)[/tex]):
[tex]\[
f(3) = 3^2 - 2 \cdot 3 - 4 = 9 - 6 - 4 = -1
\][/tex]
So, the third term is [tex]\( -1 \)[/tex].
4. Fourth term ([tex]\( n = 4 \)[/tex]):
[tex]\[
f(4) = 4^2 - 2 \cdot 4 - 4 = 16 - 8 - 4 = 4
\][/tex]
So, the fourth term is [tex]\( 4 \)[/tex].
5. Fifth term ([tex]\( n = 5 \)[/tex]):
[tex]\[
f(5) = 5^2 - 2 \cdot 5 - 4 = 25 - 10 - 4 = 11
\][/tex]
So, the fifth term is [tex]\( 11 \)[/tex].
Hence, the first five terms of the sequence [tex]\( f(n) = n^2 - 2n - 4 \)[/tex] are:
[tex]\[
-5, -4, -1, 4, 11
\][/tex]
