Option D: The first 4 terms of the sequence is -5, -3, 1, 7
Explanation:
Given that the expression is [tex]n(n-1)-5[/tex]
We need to determine the first 4 terms of the sequence.
The first 4 terms of the sequence can be determined by substituting n = 1, 2, 3, 4
1st term of the sequence:
Substituting n = 1 in the expression [tex]n(n-1)-5[/tex], we have,
[tex]1(1-1)-5[/tex]
Simplifying, we get,
[tex]1(0)-5=-5[/tex]
Thus, the 1st term of the sequence is -5
2nd term of the sequence:
Substituting n = 2 in the expression [tex]n(n-1)-5[/tex], we have,
[tex]2(2-1)-5[/tex]
Simplifying, we get,
[tex]2(1)-5\implies2-5\implies-3[/tex]
Thus, the 2nd term of the sequence is -3.
3rd term of the sequence:
Substituting n = 3 in the expression [tex]n(n-1)-5[/tex], we have,
[tex]3(3-1)-5[/tex]
Simplifying, we get,
[tex]3(2)-5\implies 6-5\implies 1[/tex]
Thus, the 3rd term of the sequence is 1.
4th term of the sequence:
Substituting n= 4 in the expression [tex]n(n-1)-5[/tex], we have,
[tex]4(4-1)-5[/tex]
Simplifying, we get,
[tex]4(3)-5\implies 12-5\implies 7[/tex]
Thus, the 4th term of the sequence is 7
Thus, the first 4 terms of the sequence is -5, -3, 1, 7
Hence, Option D is the correct answer.
