Resources tagged with: Recurrence relations

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Broad Topics > Patterns, Sequences and Structure > Recurrence relations

And So on - and on -and On

Age 16 to 18 Challenge Level:

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

Poly Fibs

Age 16 to 18 Challenge Level:

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 14 to 16 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?

2^n -n Numbers

Age 16 to 18

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

Golden Powers

Age 16 to 18 Challenge Level:

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

Production Equation

Age 16 to 18 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?