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

Problem
Primary curriculum
Secondary curriculum
### Production Equation

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### And So on - and on -and On

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Poly Fibs

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.

Age 16 to 18

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Powerful Properties

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

Age 16 to 18

Problem
Primary curriculum
Secondary curriculum
### Loopy

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Golden Powers

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

Age 16 to 18

Challenge Level