Number Patterns and Sequences

🎯 What Will We Learn Today?

Math is full of patterns! Today we'll explore number sequences — ordered lists of numbers that follow a rule — and learn how to figure out what comes next.

📚 What Is a Number Sequence?

A number sequence is a list of numbers arranged in a specific order following a rule or pattern.

🔍 How to Spot the Pattern

The big question is always: "What's happening here?"

Arithmetic Sequences（Add or Subtract the Same Amount）

2, 4, 6, 8, 10, ... （Rule: add 2）
15, 12, 9, 6, 3, ... （Rule: subtract 3）

Geometric Sequences（Multiply by the Same Amount）

1, 2, 4, 8, 16, ... （Rule: multiply by 2）
800, 400, 200, 100, ... （Rule: divide by 2 = multiply by ½）

Special Sequences

Square Numbers: 1, 4, 9, 16, 25, ... （1², 2², 3², 4², 5²）
Fibonacci: 1, 1, 2, 3, 5, 8, 13, ... （add the previous two terms）

🎮 The 4-Step Sequence Strategy

Look at the differences between neighboring numbers

Is there a pattern in the differences?

If differences aren't constant, check for multiplication or division

Use the rule you found to find the next number!

💡 Key Pattern Guide

| Differences | Type of Rule |
|-------------|-------------|
| Same difference each time | Addition or subtraction（Arithmetic） |
| Different each time but doubling | Multiplication or division（Geometric） |
| Increasing differences | Might be square numbers |

📝 Practice Problems

Find the next number:

3, 7, 11, 15, ___ （Pattern: +4）

100, 90, 80, 70, ___

2, 4, 8, 16, ___

1, 4, 9, 16, ___

What are the first five terms of the rule "start at 3, add 5 each time"?

🎮 Play a Game!

Master patterns with Swimming Otters!