list the next two numbers in the sequence ... -2,0,4,12,28
-2 + 2 = 0
0 + 4 = 4
4 + 8 = 12
12 + 16 = 28
Do you see the pattern?
What do you think the next two numbers are?
so would it be 28+18=46 and 46+20=66 right?
Nope.
Did you notice that the number you added is double the number you previously added?
2, 4, 8, 16 . . .
so basically im counting by two's?
To find the next two numbers in the sequence -2, 0, 4, 12, 28, we need to identify the pattern or rule that governs the sequence.
Let's examine the differences between consecutive terms:
0 - (-2) = 2
4 - 0 = 4
12 - 4 = 8
28 - 12 = 16
At first glance, the differences don't seem to follow a simple pattern. However, let's look at the second differences (the differences between the differences):
4 - 2 = 2
8 - 4 = 4
16 - 8 = 8
The second differences are constant, indicating that the original sequence might have a quadratic pattern.
Now, we can assume that the sequence follows a quadratic equation of the form an^2 + bn + c, where n represents the term number (starting from n = 1).
To find the coefficients, we can substitute the first few terms into the quadratic equation:
a(1)^2 + b(1) + c = -2
a(2)^2 + b(2) + c = 0
a(3)^2 + b(3) + c = 4
Simplifying these equations, we get:
a + b + c = -2 (Equation 1)
4a + 2b + c = 0 (Equation 2)
9a + 3b + c = 4 (Equation 3)
Solving this system of equations should give us the values of a, b, and c.
By solving Equations 1, 2, and 3 simultaneously, we find that:
a = 3/2
b = -7
c = 13/2
Now, we can continue the sequence by substituting n = 6 and n = 7 into the quadratic equation:
For n = 6:
a(6)^2 + b(6) + c = (3/2)(6^2) + (-7)(6) + 13/2
= 27 + (-42) + 13/2
= -2.5
For n = 7:
a(7)^2 + b(7) + c = (3/2)(7^2) + (-7)(7) + 13/2
= 49.5 + (-49) + 13/2
= 5
Therefore, the next two numbers in the sequence are -2.5 and 5.