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There is 1 NRICH Mathematical resource connected to Recurrence relations, you may find related items under Patterns, sequences and structure.
Broad Topics > Patterns, sequences and structure > Recurrence relationsInvestigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?