There are **6** NRICH Mathematical resources connected to **Recurrence relations**, you may find related items under Patterns, Sequences and Structure.

Challenge Level

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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Can you find the value of this function involving algebraic fractions for x=2000?

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A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.

Yatir from Israel wrote this article on numbers that can be written as $ 2^n-n $ where n is a positive integer.

Challenge Level

Investigate 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?

Challenge Level

You add 1 to the golden ratio to get its square. How do you find higher powers?