What are the next three terms in the sequence? -6.5,16,27...
A. 38,49,60
B. 37,47,57
C. 36,45,54
D 36,46,57
I see you kept adding 9 but how does your rule get you to 27 from 16?
Maybe if you fix your typo so the sequence starts -6, 5 you will get the correct answer.
Aren't you adding 11 in this sequence?
It’s literally easy
38,49,60
To find the next three terms in the sequence -6.5, 16, 27, we need to identify the pattern in the given numbers.
Looking closely at the given sequence, we can see that the pattern is not linear, as the difference between successive terms is not constant. Instead, the pattern seems to alternate between increasing and decreasing differences.
The first difference between the terms is 16 - (-6.5) = 22.5.
The second difference between the terms is 27 - 16 = 11.
Now, let's check the differences between the next terms:
The third difference should be 38 - 27 = 11.
The fourth difference should be 49 - 38 = 11.
Since the difference between the last two differences is the same (11), we can conclude that the pattern is likely quadratic. To confirm this, we can calculate the differences between the second differences:
The second difference between the differences is 11 - 22.5 = -11.5.
The negative value of the second difference suggests that the pattern is quadratic. Now, we can try to find the quadratic equation for the given sequence.
Let's assume the quadratic equation is of the form y = ax^2 + bx + c, where y represents the sequence terms and x represents the position of the term. Since we have three terms and three unknowns (a, b, and c), we can set up a system of equations using the terms of the sequence:
For the first term (-6.5):
a(1)^2 + b(1) + c = -6.5
For the second term (16):
a(2)^2 + b(2) + c = 16
For the third term (27):
a(3)^2 + b(3) + c = 27
Simplifying the equations, we have:
a + b + c = -6.5 ----(1)
4a + 2b + c = 16 ----(2)
9a + 3b + c = 27 ----(3)
Solving this system of equations, we find that a = 1, b = 1.5, and c = -9.5.
Therefore, the quadratic equation for the given sequence is y = x^2 + 1.5x - 9.5.
Now, let's find the next three terms by plugging in x = 4, 5, and 6 into the equation:
For x = 4:
y = (4)^2 + 1.5(4) - 9.5 = 16 + 6 - 9.5 = 12.5
For x = 5:
y = (5)^2 + 1.5(5) - 9.5 = 25 + 7.5 - 9.5 = 23
For x = 6:
y = (6)^2 + 1.5(6) - 9.5 = 36 + 9 - 9.5 = 35.5
So, the next three terms in the sequence are 12.5, 23, and 35.5.
Therefore, the correct answer is D. 36, 46, 57.