Patterns and sequences

A pattern is something that repeats or grows by a rule. Find the rule and you can tell what comes next, what comes a hundred steps later, and sometimes what happens if it goes on forever.

Step	Page	You will be able to
Play	What comes next?	Spot repeating and growing patterns and continue them
Explore	Number sequences and their rules	Describe a sequence with a rule and a table; meet square, triangle and Fibonacci numbers
Build	Adding the same amount: arithmetic sequences	Find any term with a formula and add up a long list fast
Master	Multiplying by the same amount: geometric sequences	Work with doubling and halving, growth and decay, and sums that go on forever
Beyond	Rules that call themselves, and proof by induction	Use recursion, meet the golden ratio and prove a pattern is true for every number