What are the first four terms of the sequence represented by the expression n(n – 2) – 3?
A. –5, –2, 1, 4
B. –4, –3, 0, 5
C. –3, 0, 3, 6
D. –2, 0, 2, 4
To find the first four terms of the sequence represented by the expression n(n – 2) – 3, we substitute n = 1, 2, 3, and 4.
For n = 1: 1(1 – 2) – 3 = –2
For n = 2: 2(2 – 2) – 3 = –3
For n = 3: 3(3 – 2) – 3 = –3
For n = 4: 4(4 – 2) – 3 = 5
Therefore, the first four terms are: –2, –3, –3, 5.
The answer is B. –4, –3, 0, 5.
To find the first four terms of the sequence represented by the expression n(n – 2) – 3, we will substitute the values of n starting from 1 up to 4 into the expression and evaluate it.
Let's go through each option and check if it matches the expression for the given values of n:
A. Substituting n = 1, 2, 3, 4 into the expression n(n – 2) – 3 gives us:
1(1 – 2) – 3 = -2 - 3 = -5
2(2 – 2) – 3 = 0 - 3 = -3
3(3 – 2) – 3 = 3 - 3 = 0
4(4 – 2) – 3 = 8 - 3 = 5
Therefore, option A gives us the terms -5, -3, 0, and 5, which don't match the given sequence.
B. Substituting n = 1, 2, 3, 4 into the expression n(n – 2) – 3 gives us:
1(1 – 2) – 3 = -1 - 3 = -4
2(2 – 2) – 3 = 0 - 3 = -3
3(3 – 2) – 3 = 3 - 3 = 0
4(4 – 2) – 3 = 8 - 3 = 5
Therefore, option B gives us the terms -4, -3, 0, and 5, which match the given sequence.
C. Substituting n = 1, 2, 3, 4 into the expression n(n – 2) – 3 gives us:
1(1 – 2) – 3 = -1 - 3 = -4
2(2 – 2) – 3 = 0 - 3 = -3
3(3 – 2) – 3 = 3 - 3 = 0
4(4 – 2) – 3 = 8 - 3 = 5
Therefore, option C gives us the terms -4, -3, 0, and 5, which don't match the given sequence.
D. Substituting n = 1, 2, 3, 4 into the expression n(n – 2) – 3 gives us:
1(1 – 2) – 3 = -1 - 3 = -4
2(2 – 2) – 3 = 0 - 3 = -3
3(3 – 2) – 3 = 3 - 3 = 0
4(4 – 2) – 3 = 8 - 3 = 5
Therefore, option D gives us the terms -4, -3, 0, and 5, which don't match the given sequence.
In conclusion, the correct answer is B. The first four terms of the sequence represented by the expression n(n – 2) – 3 are -4, -3, 0, and 5.
To find the first four terms of the sequence represented by the expression n(n – 2) – 3, we substitute values of n starting from 1 and continuing in order.
Let's substitute n = 1:
1(1 – 2) – 3 = 1(-1) - 3 = -1 - 3 = -4
Now, let's substitute n = 2:
2(2 – 2) – 3 = 2(0) - 3 = 0 - 3 = -3
Continuing, let's substitute n = 3:
3(3 – 2) – 3 = 3(1) - 3 = 3 - 3 = 0
Finally, let's substitute n = 4:
4(4 – 2) – 3 = 4(2) - 3 = 8 - 3 = 5
So, the first four terms of the sequence represented by the expression n(n – 2) – 3 are: -4, -3, 0, 5.
Therefore, the correct answer is B. –4, –3, 0, 5.