This is a great example of the requirement for proof and reasoning: any of the nth term expressions would fit the first three terms of 1, 2 and 4, yet depending on the situation it is likely that some of the expressions would be inappropriate.
It is also reminded me of an idea of Lucia Handley, using cubes to investigate sequences.
The Sequence Zoo
The lesson began with an arrangement of animals: giraffes, pigs and cows/zebras. Pupils could then be challenged to work out what the baby of each animal looked like, or to work out whether they could give the number of bricks required to make a species, given its height.
Alternatively, the animals in the image above could be used and pupils had to find out which animal had grown out of sequence.
The cow/zebra is particularly interesting, as you could look either at total number of blocks, or the white / black components.
Thanks Lucia!
