Need to find the "nth" term in a patterm

Using the following data, need to see if I can come up with an equation to find "y" in the 100th pattern.

X Y
1 4
2 12
3 24
4 40
5 60
6 84
7 112
8 144

I can see the pattern having to multiply "x" by adding a consectutive multiple of 4 each time, but can't seem to find an equation to find the number in the 100th pattern.

X Y
1 4 = 4·1
2 12 = 4·3
3 24 = 4·6
4 40 = 4·10
5 60 = 4·15
6 84 = 4·21
7 112 = 4·28
8 144 = 4·36

If you are familiar with triangular numbers, then you recognize that:

\(\displaystyle y(x)=4\left(\dfrac{x(x+1)}{2} \right)=2x(x+1)\)

Otherwise, if you see that the second difference is constant, then you know the closed-form is quadratic:

\(\displaystyle y(x)=Ax^2+Bx+C\)

Now, use the initial values to determine the parameters:

\(\displaystyle y(1)=A+B+C=4\)

\(\displaystyle y(2)=4A+2B+C=12\)

\(\displaystyle y(3)=9A+3B+C=24\)

Solving this system, we find:

\(\displaystyle A=2,\,B=2,\,C=0\)

Hence:

\(\displaystyle y(x)=2x^2+2x=2x(x+1)\)