Concept 1 of 6
Number Series: Spot the Rule
Today's big idea
Find the gap rule between the numbers, then use it to predict the next.
In 2, 5, 8, 11 the gaps are all +3, so the rule is add 3 and next comes 14.
How it works
👀 What's going on?
A number series is a list with a rule hidden inside it. Nobody tells you the rule. You work it out from the numbers you can see, then use it to say what comes next.
💡 Here's the trick
Look at the series above: 2, 5, 8, 11. Writing the gap under each pair shows +3 each time, so the rule is add 3. The next number is 11 + 3 = 14. The gaps are where the rule hides. Equal gaps mean adding or subtracting, and growing gaps mean something else is going on.
🪄 How to do it
- 1.Write the gap under each pair of numbers, the way the picture above does.
- 2.Look for the pattern in those gaps.
- 3.Apply that rule to the last number to get the next one.
✍️ Try it
Find the next number in 3, 7, 11, 15, ? Then find the next in 1, 4, 9, 16, ? The gaps behave quite differently.
The first has gaps of +4, +4, +4, so the next is 15 + 4 = 19. The second has gaps of +3, +5, +7, each one growing by 2, so the next gap is +9 and the answer is 25. Those are the square numbers.
⚠️ Watch out
You might be thinking a series with growing gaps has no rule at all. It has one, just a rule about the gaps rather than about the numbers. Write the gaps out in a row of their own and look at those instead.
🌟 Why this matters
Bus timetables, savings that grow each week and the seat numbers along a stadium row all follow rules like this. Spotting the rule lets you jump ahead without listing everything in between.
Exam tip: Write the gaps down rather than holding them in your head, because a mis-remembered gap is the usual cause of a wrong answer.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What comes next: 6, 10, 14, 18, ?”
- 1
Find the gaps
10−6 = 4. 14−10 = 4. 18−14 = 4.
- 2
Spot the rule
Every gap is +4. Constant gap → adding.
- 3
Apply once more
18 + 4 = 22
- 4
Next ✓
Next number = 22
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Reveal the jump between each pair, spot the rule, then extend the series.
SERIES · ROUND 1 OF 3
What is the jump from 4 to 9?
Quick check
✅ VERIFICATION
Find the next number: 1, 3, 9, 27, ?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Repeating Patterns
Spot the repeating chunk, then extend it or divide to jump to slot 50.