I now understand exactly what I have to do but I am having trouble finding a formula for something. I need to find a formula that will work with any number.
I am finding the volume of a 3d cross- shape. Here are my results so far:

        Term Number      0   1    2    3     4      5

        nth term         1    7   25   63   129    231

        first diff          6   18   38   66     102

        2nd diff              12    20   28   36

        3rd diff                 8     8    8

        

I can't seem to find a formula that will work with any number. Any help would be much appreciated.

Jenny

Hi Jenny,

Since the third difference is a constant the n^th term is a cubic in n. That is

x_n = a n³ + b n² + c n + d

for some a, b, c and d.

You can use the fact that you know x₀, x₁, x₂, x₃ and x₄ to set up a system of four linear equations for a, b, c and d. When I did it I found

x_n = ⁴/₃ n³ - 2 n² + ⁸/₃ n -1

Penny

Go to Math Central