inite difference formulas can be ve

inite difference formulas can be very useful for extrapolating a finite amount of data in an attempt to find the general term. Specifically, if a function f(n) is known at only a few discrete values n=0, 1, 2, ... and it is desired to determine the analytical form of f, the following procedure can be used if f is assumed to be a polynomial function. Denote the nth value in the sequence of interest by a_n. Then define b_n as the forward difference Delta_n=a_(n+1)-a_n, c_n as the second forward difference Delta_n^2=b_(n+1)-b_n, etc., constructing a table as follows