Concept 1 of 6
Number Series: Find the Hidden Rule
Today's big idea
Write the gap under each pair, then read the gaps: equal, growing, or a fixed multiple.
Gaps that are not equal are still a pattern, so look at the gaps between the gaps.
How it works
👀 What's going on?
A row of numbers marches across the page and one of them is missing. It looks like a guessing game, but it never is. Every series is built by a rule, and the rule leaves footprints.
💡 Here's the trick
Look at the series above. Write the gap under each pair of terms and the rule shows itself. Equal gaps mean add or subtract. A fixed multiple means multiply. Gaps that grow mean the rule grows too.
🪄 How to do it
- 1.Write the gap under each pair, as in the series above.
- 2.Decide if the gaps are equal, growing, or hiding a multiply rule.
- 3.Apply that rule one more time to get the missing term.
✍️ Try it
Find the next number in 9, 18, 36, 72, ? Then find the next number in 1, 4, 8, 13, 19, ?
Each term doubles, so the next one is 72 × 2 = 144. In the second series the gaps run +3, +4, +5, +6, so the next gap is +7 and the answer is 26.
⚠️ Watch out
You might be thinking a series must always climb. Plenty of them fall, and some do both. Check the direction of every gap before you name the rule, not just the first gap.
🌟 Why this matters
Bus timetables, shoe sizes and the price board at a stall all step up by a fixed amount. Spot the step once and you can read the rest without checking every line.
Exam tip: Write the gaps down on paper. A rule you can see beats a rule you try to hold in your head.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Find the next number: 5, 11, 23, 47, ?”
- 1
Write the gaps
11−5 = 6, 23−11 = 12, 47−23 = 24. Gaps are doubling — not a simple add. 🔍
- 2
Test ×2 then +1
5×2+1 = 11 ✓, 11×2+1 = 23 ✓, 23×2+1 = 47 ✓. Rule found!
- 3
Apply once more
47 × 2 + 1
- 4
Answer ✓
= 95
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap each number in the correct order — spot the pattern!
NUMBER SERIES · ROUND 1 OF 3
What comes next? 2, 6, 18, 54, __
Quick check
✅ VERIFICATION
Find the next number: 7, 8, 11, 16, 23, ?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Letter Series
A=1 … Z=26. Find the jump, add it, convert back.