Solve Finite Difference: Find Constant Equation

[Meh]

Hello there...I'm currently stuck with a problem regarding finite differences. The question asks for me to come up with an equation to find the constant of the finite difference. An example would be...Let's take the equation y=10x^4 and the constant is 240. Any hints as to where to start or anyone feeling generous enough to just give me the equation?

 

[0rthodontist]

well, I don't have any proof of this in hand but you could notice that
10 * 4 * 3 * 2 * 1 = 240

 

[HallsofIvy]

I think what you are doing is finding repeated differences:

x f(x) $\Delta x$ $\Delta^2 x$
1 10 150
2 160 640
3 810 1750 1940
4 2560 3690
5 6250

 

[Meh]

Thank Orthodontist and HallsofIvy, I think Ortho is on the right track...Still having a problem with coming up with an equation.