# Resources tagged with: Recurrence relations

### There are 6 results

Broad Topics >

Patterns, Sequences and Structure > Recurrence relations

##### 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 16 to 18 Challenge Level:

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

##### 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.

##### 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?

##### 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?

##### Age 16 to 18 Challenge Level:

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