Have a play around with this task, and please share any questions, extensions, simplifications, modifications, or lines of inquiry in the comment box below. The idea is to collect loads of suggestions that can then be used for effective differentiation. The full set of these tasks, along with additional notes, can be found here: http://www.mrbartonmaths.com/richtasks.htm
This rich task from the legendary Mr Barton will really spark students interest. Starting with linear sequences, students form a pair of simultaneous equations and solve them. What happens if they start with 2 different sequences? Try it yourself and see if your curiosity isn't piqued!