n Learning and Teaching Mathematics - Generalising cubic sequences using a filtration method

Abstract

In my experience, most learners have become quite proficient at determining the general expression for a given quadratic sequence. One can build on this proficiency to generalise cubic sequences of the form Tn = an³ + bn² + cn + d by using a filtration technique. The filtration method provides a means of "filtering out" the cubic part of the general expression for a cubic sequence leaving behind a quadratic "residue", a general expression for which can be found using any number of conventional approaches.