The nth term of a sequence is given by the formula n^3 + 11n . Find
the first four terms of the sequence given by this formula and the
first term of the sequence which is bigger than one million. Prove
that all terms of the sequence are divisible by 6.

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?

Double Trouble

Stage: 4 Challenge Level:

Charlie has been adding fractions in the sequence $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \dots$ where each fraction is half the previous one: