This problem demonstrates how a formula can be derived from the context (rather than "pattern-spotting") in a variety of ways.
It also provides practice in the manipulation of algebraic symbols and generates generalities that can promote discussions on equivalent symbolic forms.

A teacher comments:
This was a good opportunity to practise simple and more difficult sequences and generation of formulae, ranging from linear to cubic. All pupils were able to access the problem up to (and beyond) their own "natural" ability (Year 9 set 2).