My son is very interested nowadays in looking for patterns.
He started with simple patterns like ABCABC ..., then developed to complex ones like AABCCCAABCCC, (where A, B & C can stand for colors, shapes, letters, numbers, objects, animals, etc... ) or even combinations of these. Then he started applying the concept to numerics like 1,3,5,7,.... or 11,22,33,.... or even 120,230,340,....
It is an interesting game to try to solve the rule/formula and guess the whole series.
For example: The series 3,5,7, ... is based on the formula: 2n+1 where n=1,2,3,...
More info about sequences can be found at
http://www.mathsisfun.com/algebra/sequences-series.htmlMore series/patterns examples are most welcome.
Rima