what happens if you start with 2 numbers, produce a next number which is the average of these two and then iterate this process?
[sometimes this is know by the (fictitious) name 'Littov's' chain]
all number pairs reach a limit, which has a neat generalisation
students might explore this for their own two starting values, working on paper initially
it is also very easy to set up a formula that can be dragged down on a spreadsheet (using abs for the absolute value)
what happens for (4, 7)? for (10, 4)? for (2, 8)? plus some other ordered pairs....
mathsonline has a version of this task ('the mean series') available to non-members, either as an Excel sheet or online. The Excel sheet contains a graph, showing how the values home in (smooth) to their limit value.
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