How to Decipher Patterns: A Guide to Mathematical Sequences
A sequence is an ordered list of numbers that follows a rule. In an arithmetic sequence you add the same number each time (2, 5, 8, 11, …), so aₙ = a₁ + (n − 1)d. In a geometric sequence you multiply by the same number each time (3, 6, 12, 24, …), so aₙ […]
How to Master Inductive Reasoning from Patterns
Inductive reasoning draws a general rule from specific observations. It suggests what is probably true rather than proving it, which is exactly why a conjecture reached inductively still needs a deductive proof. Worked examples: inductive reasoning from a pattern Practice questions on inductive reasoning Given the sequence: (3, 6, 9, 12…) what might be the […]