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6;15; x; 45;....... is a quadratic number pattern (sequence). Determine the value of x. ​

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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:

https://brainly.com/question/13729904

#SPJ1

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