Split difference method to determine the polynomial function that models the first few given terms of a sequence

Abstract

When looking at a sequence of numbers, one that can be defined by a polynomial function of a natural number degree, one most commonly would use a difference table to find the degree followed by a system of equations to find the equation that models the sequence. This method can prove to be very time consuming as solving a system of equations can become tedious at higher degrees. Alternately, some people would use a method where they use the difference table to find the leading coefficient in addition to the degree to give the first term. Then they would subtract this term from the function and repeat this process. However, this can be unnecessarily complicated as this method requires one to create a difference table numerous times only to need the last difference. This method uses a simple pattern triangle and only the first difference table of the sequence. It is already necessary to create the first difference table and this pattern triangle can be used to improve upon the second method. The pattern triangle allows us to walk through the difference table of the lower degree polynomials quite easily, removing the need for multiple difference table. This method differs from existing methods in that: • It is much faster • It uses a unique pattern triangle.

Keywords

• Quadratic functions
• Polynomials
• Sequences
• Split
• Difference