Which of the following number sequences could be produced by the expression `2x + x^2`?
correctA. 3, 8, 15, 24
B. 1, 3, 5, 7
C. 1, -1, -3, -5
D. 2, 7, 14, 21
what made you think of 1
Well, let's see. If we plug in the first number in sequence A, which is 3, into the expression 2x + x^2, we get 2(3) + (3)^2 = 6 + 9 = 15. So A checks out!
Now, if we plug in the first number in sequence B, which is 1, into the expression 2x + x^2, we get 2(1) + (1)^2 = 2 + 1 = 3. So B is also a winner!
But if we try the first number in sequence C, which is 1, we get 2(1) + (1)^2 = 2 + 1 = 3. Oops! That's not right, so C is out!
Finally, if we plug in the first number in sequence D, which is 2, we get 2(2) + (2)^2 = 4 + 4 = 8. So D is good to go!
So the sequences that could be produced by the expression 2x + x^2 are A and D. Keep up the good work!
To determine which of the number sequences could be produced by the expression `2x + x^2`, we can substitute values of x into the expression and see if the resulting values match any of the sequences.
Let's go through the options one by one:
A. 3, 8, 15, 24
Let's test x = 1:
2(1) + (1)^2 = 2 + 1 = 3
Let's test x = 2:
2(2) + (2)^2 = 4 + 4 = 8
Let's test x = 3:
2(3) + (3)^2 = 6 + 9 = 15
Let's test x = 4:
2(4) + (4)^2 = 8 + 16 = 24
All the values match the sequence, so A could be the correct answer.
B. 1, 3, 5, 7
Let's test x = 1:
2(1) + (1)^2 = 2 + 1 = 3
Let's test x = 2:
2(2) + (2)^2 = 4 + 4 = 8
The first two values match the sequence, but the rest do not. Therefore, B is not the correct answer.
C. 1, -1, -3, -5
Let's test x = 1:
2(1) + (1)^2 = 2 + 1 = 3
Let's test x = -1:
2(-1) + (-1)^2 = -2 + 1 = -1
The first two values match the sequence, but the rest do not. Therefore, C is not the correct answer.
D. 2, 7, 14, 21
Let's test x = 1:
2(1) + (1)^2 = 2 + 1 = 3
Let's test x = 2:
2(2) + (2)^2 = 4 + 4 = 8
The first two values match the sequence, but the rest do not. Therefore, D is not the correct answer.
Based on our analysis, the correct answer is A. 3, 8, 15, 24.
2(1)+(1)^2
2+1
=3
2(2)+(2)^2
4+4
=8
You had me with 2*1+1^2 = 3
since A was the only sequence starting with 3.