Mathematical Reasoning · Quick Reference

Pattern Recognition Cheat Sheet

Mathematical Reasoning · Lesson 2/4

In one line: pattern recognition trains you to spot the hidden rule behind a sequence — a skill at the heart of both puzzles and real mathematical discovery.

Key Ideas

1Number Series. A sequence of numbers following a consistent rule, such as adding a fixed amount, multiplying by a factor, or alternating between operations.

2Arithmetic Patterns. Each term differs from the previous one by a constant amount (a common difference).

3Geometric Patterns. Each term is found by multiplying the previous one by a constant factor (a common ratio).

4Letter Series. Sequences of letters following a rule based on their position in the alphabet, such as skipping a fixed number of letters each time.

5Combined/Alternating Patterns. Some sequences alternate between two separate rules or interleave two simpler sequences together.

Worked Examples

Find the next number: 3, 7, 11, 15, ...

Find the next number: 2, 6, 18, 54, ...

162

Find the next letter: A, C, E, G, ...

Practice Yourself

Find the next number: 5, 10, 15, 20, ...

Find the next number: 1, 3, 9, 27, ...

Find the next number: 100, 90, 80, 70, ...

Find the next letter: B, D, F, H, ...