A quadratic pattern has a third term equal to 2,a fourth term equal to -2 and the sixth term equal to-16 . calculate the second difference of this quadratic pattern
oops. I missed the skipped term
2 -2.... -8.. -16
..-4..-6....-8
......-2...-2
To calculate the second difference of a quadratic pattern, we first need to find the common difference.
Let's denote the first term of the quadratic pattern as "a", and the common difference as "d".
Given that the third term is equal to 2, we have:
a + 2d = 2 ----(Equation 1)
Similarly, for the fourth term being -2, we get:
a + 3d = -2 ----(Equation 2)
Lastly, for the sixth term being -16, we have:
a + 5d = -16 ----(Equation 3)
Now, we have a system of three equations with three unknowns. We can solve this system of equations to find the values of "a" and "d".
To solve the system, we can use the method of substitution or elimination. Here, let's use the method of elimination:
Subtract Equation 1 from Equation 2:
(a + 3d) - (a + 2d) = -2 - 2
Simplifying, we get:
d = -4 ----(Equation 4)
Now that we have found the value of "d", we can substitute it back into any of the three original equations to find the value of "a". Let's use Equation 1:
a + 2(-4) = 2
a - 8 = 2
a = 10 ----(Equation 5)
Therefore, we have found the values of "a" and "d" as a = 10 and d = -4, respectively.
Now, to calculate the second difference, we need to find the difference between the differences of consecutive terms. We can do this by subtracting the common difference "d" from the next common difference.
The first difference is "d", which is -4.
The second difference is -4 - (-4) = 0.
Hence, the second difference of this quadratic pattern is 0.
2 -2 -16
.-4.-14
.....-10