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## 'Loopy' printed from http://nrich.maths.org/

The terms $a_1, a_2, a_3,...\ a_n,...\ $ of a sequence are given
by: $$a_n =\frac{1+a_{n-1}}{a_{n-2}}.$$ Investigate the sequences
you get when you choose your own first two terms. Make a conjecture
about the behaviour of these sequences. Can you prove your
conjecture? Investigate the sequences.