Solving a system of equations, we conclude that the value of x is 28.
How to determine the value of x?
Here we have the quadratic number pattern:
6, 15, x, 45, ...
First, we have that:
15 - 6 = 9
So 9 is the first difference.
Then we will have:
x = 15 + 9 + a
(where a is the second difference, constant of the sequence).
And:
45 = x + 9 + a + a
Then we have a system of equations:
x = 15 + 9 + a
45 = x + 9 + a + a
We can isolate a on the first equation:
a = x - 24
We can replace that in the other equation:
45 = x + 9 + 2a
45 = x + 9 + 2*(x - 24)
Now we can solve that for x:
45 - 9 = x + 2*(x - 24)
36 = 3x - 48
36 + 48 = 3x
84 = 3x
84/3 = x = 28
The value of x is 28.
If you want to learn more about systems of equations:
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