Finding the nth term rule of a quadratic sequence

A complete lesson on finding the nth term rule of a quadratic sequence. This primarily focuses on one method (see cover slide), although I’ve thrown in a different method as an extension. I always cover linear sequences in a similar way and incorporate a recap on this within the lesson.

Starter:
To prepare for the main part of the lesson, pupils try to solve a system of three equations with three unknowns.

Main:

• A recap on finding the nth term rule of a linear sequence, to prepare pupils for a similar method with quadratic sequences.
• Examples on the core method, followed by a worksheet with a progression in difficulty for pupils to practice. I’ve included two versions of the worksheet - a simple list of questions that could be projected, or a much more structured worksheet that could be printed. Worked solutions are included.
• A worked example of an alternative method, that could be given as a handout for pupils who finish early to try on the questions they’ve already done.

Plenary:
A proof of why the method works. I’d much rather show this at the start of the lesson, but in my experience this usually overloads students and puts them off if used too soon!

Please review if you buy as any feedback is appreciated!