Number Sequences Lesson: Recognizing and Continuing Patterns

Lesson Overview

• What Is a Number Sequence?
• Increasing Sequences (Adding Numbers)
• Decreasing Sequences (Subtracting Numbers)
• Skip Counting Patterns
• Multiplication Patterns (Geometric Sequences)
• Finding the Rule in a Sequence
• Finding the Missing Number
• Sequences with Changing Differences
• Real-Life Number Sequences
• Practice Reading and Naming Sequences

Numbers follow patterns just like music and nature. These patterns are called number sequences, and learning how to recognize them helps us solve math problems faster, build strong number sense, and discover how numbers work together.

In this lesson, you'll learn about different types of number sequences, how to find missing numbers, and how to continue a sequence using rules. You'll also practice reading number patterns that increase, decrease, or multiply. Let's explore how numbers line up, jump, and grow!

What Is a Number Sequence?

A number sequence is a list of numbers that follow a certain rule. The numbers are arranged in a specific order based on what happens between them.

Some rules involve:

• Adding the same number each time
  
• Subtracting the same number each time
  
• Multiplying or dividing
  
• Or even changing the rule slightly as the sequence continues
  

Example:
2, 4, 6, 8, 10 - This is a sequence that adds 2 each time.

Understanding number sequences helps you become better at solving math problems, predicting patterns, and building number sense.

Increasing Sequences (Adding Numbers)

An increasing sequence means each number is getting larger.

The increase happens when you add the same number over and over.

Example:
1, 3, 5, 7, __
We add 2 each time. 7 + 2 = 9

So the next number is 9.

How to spot an increasing pattern:

• Look at how much each number changes.
  
• Is the same number being added again and again?
  

Increasing patterns are common in skip counting and are the basis for multiplication tables.

Take This Quiz:

Number Sequences Quiz

Decreasing Sequences (Subtracting Numbers)

A decreasing sequence means each number is getting smaller.

This happens when you subtract the same number again and again.

Example:
12, 10, 8, 6, __
We subtract 2 each time. 6 - 2 = 4

So the next number is 4.

Clue: If the numbers are dropping, it's likely a decreasing sequence using subtraction.

Skip Counting Patterns

Skip counting is a fun and fast way to count numbers by jumping ahead by a fixed number.

Examples of skip counting:

Skip counting is used in:

• Telling time (counting by 5s on a clock)
  
• Counting money (nickels, dimes)
  
• Multiplication (2 times table, 5 times table)
  

It's one of the best ways to understand multiplication and fast addition.

Multiplication Patterns (Geometric Sequences)

Some number sequences grow quickly using multiplication instead of addition.

These are called multiplying patterns or geometric sequences.

Example: 2, 4, 8, 16, __
Here, each number is multiplied by 2.
16 × 2 = 32

Multiplying sequences grow faster than adding ones. Watch out for them when the numbers are getting big quickly.

Finding the Rule in a Sequence

To solve or continue a number sequence, first figure out the rule.

Steps to find the rule:

1. Look at the difference between two numbers.
   
2. Is the number increasing or decreasing?
   
3. Try adding, subtracting, or multiplying to see what fits.
   

Example:
5, 10, 15, 20
Each number increases by 5 → Rule: Add 5

Example 2:
100, 90, 80, 70
Each number decreases by 10 → Rule: Subtract 10

Identifying the rule helps you predict what comes next.

Finding the Missing Number

Sometimes, a number is missing from the sequence. To find it, use the rule you've discovered.

Example:
3, 6, __, 12, 15
The difference between 3 and 6 is +3
Between 12 and 15 is also +3
So the missing number is: 6 + 3 = 9

The complete sequence is: 3, 6, 9, 12, 15

Missing number problems test your pattern recognition and reasoning skills.

Take This Quiz:

Maths quiz- UNIT 2. Sequences and Series of Real Numbers

Sequences with Changing Differences

Not all sequences change by the same number every time. Some have growing differences.

Example:
2, 4, 7, 11, __
Look at how it changes:

• 4 - 2 = 2
  
• 7 - 4 = 3
  
• 11 - 7 = 4
  

So the next difference is +5
11 + 5 = 16

Changing patterns like this are called increasing difference sequences.

Real-Life Number Sequences

We use number patterns in many everyday situations.

Understanding these patterns helps us predict, plan, and solve problems in everyday life.

Practice Reading and Naming Sequences

Let's practice figuring out what kind of sequence each example is:

1. 10, 20, 30, 40
Pattern: Add 10 → Arithmetic sequence

2. 2, 4, 8, 16, 32
Pattern: Multiply by 2 → Geometric sequence

3. 15, 13, 11, 9, 7
Pattern: Subtract 2 → Decreasing sequence

4. 5, 10, 17, 26, 37
Pattern: Add 5, then add 7, then 9, then 11 → Growing difference

By learning to read number patterns, you become a stronger and faster problem solver.