What Are the Coefficients in a Cubic Sequence Formula?

[sara_87]

I am completely stuck on working out cubic sequences.. i know its sumthing along the lines of an3+bn2+cn+d but i don't know what each part means as in what does a = b= c= and d=?. And how to go about working it out. I have this sequence which i would like to work out :

1,4,10,20,35

 

[dodo]

Maybe it would be useful to think how would you do the same, in a simple case which you can probably solve already.

Suppose you are given the linear sequence 1, 4, 7, 10, 13 ... Could you tell the values of 'a' and 'b' in the expression an+b ? How did you find 'a'? And how does the value of 'b' relate to the range of n? (that is, did you start n from 0 or from 1?)

After tackling this simpler case, you can try to find a, b, c in the quadratic expression an^2 + bn + c, for the new sequence 1, 4, 8, 13, 19. If you can move from the linear to the quadratic case, then you'd get the insight to work out the original cubic problem.