Sequences with Polynomial nth Term Formulae - An Investigation

This series of 8 steps starts by leading students to the discovery of how to find a linear rule for a sequence. This is then developed to second, third and fourth order rules. As the steps progress I have removed more and more scaffolding to enable the students room to discover and think. The final three steps challenge the students to discover the formulae for the sums of the first n integers, square numbers and cube numbers. A knowledge of simultaneous equations in two variables is required, this needs to be extended into three and perhaps four if students progress. I have used it with great success with able Year 10 students. It encouraged enquiry and gave the class lots of good algebra practice.