Number sequences
Continue sequences by adding, subtracting, multiplying or dividing.
Quick answer
You can continue a number sequence by finding the pattern and then using that pattern to work out the next numbers.
Learning outcome
By the end of this page, you will be able to find the pattern in a number sequence and use it to continue the sequence.
- You can spot what comes next in a sequence
- You can explain how the numbers in a sequence change
- You can write the next few numbers in a sequence
- You can use a pattern to solve simple maths problems
Why this matters
Number sequences help you understand how numbers work together and predict what comes next. This skill is useful in many places:
- When you're counting money or sharing snacks
- When you're playing games and scoring points
- When you're planning how long it takes to get to school
- When you're learning about patterns in science or art
- When you're getting ready for more advanced maths like algebra
Sequences are like puzzles that help your brain think logically and make connections. The more you practice, the better you get at spotting patterns and solving problems quickly.
How it works
Number sequences are a list of numbers that follow a rule. Here's how to find the pattern:
- Look at the first few numbers in the sequence
- Find the difference between each number
- See if the difference is always the same
- Use that difference to find the next numbers
Let's start with a simple example:
Sequence: 2, 4, 6, 8, ?
Step 1: Look at the numbers: 2, 4, 6, 8
Step 2: Find the difference between each number:
- 4 - 2 = 2
- 6 - 4 = 2
- 8 - 6 = 2
Step 3: The difference is always 2, so the pattern is "add 2"
Step 4: Add 2 to 8 to get the next number: 8 + 2 = 10
So the sequence is: 2, 4, 6, 8, 10
Examples you can see
Let's look at more examples of number sequences and how to solve them:
Example 1: Adding Pattern
Sequence: 5, 8, 11, 14, ?
Find the difference:
- 8 - 5 = 3
- 11 - 8 = 3
- 14 - 11 = 3
The pattern is "add 3". Next number: 14 + 3 = 17
Complete sequence: 5, 8, 11, 14, 17
Example 2: Subtracting Pattern
Sequence: 20, 17, 14, 11, ?
Find the difference:
- 17 - 20 = -3
- 14 - 17 = -3
- 11 - 14 = -3
The pattern is "subtract 3". Next number: 11 - 3 = 8
Complete sequence: 20, 17, 14, 11, 8
Example 3: Multiplying Pattern
Sequence: 2, 4, 8, 16, ?
Find the difference:
- 4 ÷ 2 = 2
- 8 ÷ 4 = 2
- 16 ÷ 8 = 2
The pattern is "multiply by 2". Next number: 16 × 2 = 32
Complete sequence: 2, 4, 8, 16, 32
Example 4: Mixed Pattern
Sequence: 1, 3, 6, 10, ?
Find the differences:
- 3 - 1 = 2
- 6 - 3 = 3
- 10 - 6 = 4
The differences are 2, 3, 4 - they are increasing by 1 each time.
Next difference should be 5. Next number: 10 + 5 = 15
Complete sequence: 1, 3, 6, 10, 15
Try it as a mini adventure
Adventure: The Pattern Detective
You are a detective who needs to solve a mystery! Someone has left a trail of numbers that seem to be hiding a secret message. You need to find the pattern to uncover the next numbers in the sequence.
Here's your first clue:
Clue 1: 3, 6, 9, 12, ?
What comes next? You need to find the pattern and solve it.
Clue 2: 15, 12, 9, 6, ?
What comes next? Look at the differences.
Clue 3: 1, 2, 4, 8, ?
What comes next? This one is multiplying!
Clue 4: 10, 13, 17, 22, ?
What comes next? This one is tricky - look at the differences carefully.
Can you solve all four clues and become the Pattern Detective?
Common mistakes
- Mistake: Thinking the pattern is always adding the same number
- Why it happens: Children might only look at the first few numbers and not check if the pattern continues
- Fix: Always check that the pattern works for all numbers in the sequence
- Mistake: Getting confused when numbers get bigger or smaller
- Why it happens: When subtracting, children might think a bigger number minus a smaller number gives a negative result
- Fix: Remember that the pattern must be consistent - if it's subtracting, all differences should be negative numbers
- Mistake: Forgetting to check the rule for the last few numbers
- Why it happens: Sometimes children are excited to find the answer and skip checking
- Fix: Always double-check your rule by applying it to the last few numbers
Parent and carer guide
Helping your child with number sequences is fun and easy:
- Start simple: Begin with sequences that add or subtract the same number
- Use real objects: Use counters, blocks, or toys to show the pattern
- Ask questions: "What do you notice about these numbers?" or "How are they changing?"
- Make it fun: Turn sequences into games or challenges
- Be patient: Let your child work through it without rushing
- Encourage checking: Ask them to verify their pattern works
- Use everyday examples: Point out patterns in nature, sports, or cooking
- Don't worry about speed: Focus on understanding, not quick answers
- Give praise: Celebrate when they spot a pattern correctly
- Keep it light: Make it feel like a game, not a test
Remember: It's normal for children to make mistakes. These help them learn!
Practice questions
- Complete the sequence: 4, 8, 12, 16, ?
- Complete the sequence: 25, 20, 15, 10, ?
- Complete the sequence: 3, 6, 12, 24, ?
- Complete the sequence: 1, 4, 9, 16, ?
- Complete the sequence: 50, 45, 40, 35, ?
Answers:
- 20 (add 4)
- 5 (subtract 5)
- 48 (multiply by 2)
- 25 (add consecutive odd numbers: 1, 3, 5, 7, 9)
- 30 (subtract 5)
FAQ
What is a number sequence?
A number sequence is a list of numbers that follow a pattern or rule.
How do I know what pattern to look for?
Look at the difference between consecutive numbers. If the differences are the same, it's a simple pattern. If not, look for multiplication or other patterns.
Can sequences go backwards?
Yes! Sequences can go up or down. For example, 10, 7, 4, 1 is a sequence that goes down by 3 each time.
What if I can't see the pattern?
Try looking at the differences between numbers. If that doesn't help, try looking for multiplication or division patterns.
Why do we learn about number sequences?
Sequences help us predict what comes next, which is useful in many real-life situations. They also prepare us for more advanced maths like algebra and equations.