Mathmatical pattern
4,6,9,13,18
I need formula as in y=x....
We showed you the mathematical pattern.
What do y and x represent?
I don't know what formula you need.
I need an equation because I have to graph the change on a number line.
y = (x^2 + x)/2 + 3
if x=5 for term5
y = (25+5)/2 + 3 = 18
To find a mathematical pattern in the given sequence 4, 6, 9, 13, 18, we need to first identify the relationship between the terms.
Let's calculate the differences between consecutive terms:
6 - 4 = 2
9 - 6 = 3
13 - 9 = 4
18 - 13 = 5
The differences between the terms are increasing by 1. This indicates that the sequence might have a quadratic pattern.
To verify this, let's calculate the second differences:
3 - 2 = 1
4 - 3 = 1
5 - 4 = 1
The second differences are constant, which confirms a quadratic relationship.
Now, let's try to find a quadratic formula in the form of y = ax^2 + bx + c.
To find 'a', we divide the second difference by 2:
a = 1 / 2 = 0.5
Next, let's find 'b'. We can calculate the first difference:
3 - 2 = 1
4 - 3 = 1
5 - 4 = 1
Since this sequence is increasing by a constant value of 1, 'b' will be the same as the first difference of the original sequence:
b = 1
Finally, let's find 'c'. We can use any term from the original sequence and substitute the 'x' value into the formula.
Using the first term (4), when x = 1:
y = 0.5(1^2) + 1(1) + c
4 = 0.5 + 1 + c
4 = 1.5 + c
c = 4 - 1.5
c = 2.5
Therefore, the formula for this sequence is: y = 0.5x^2 + x + 2.5