11+ Verbal reasoning · Topic explained
Number series
What comes next: 2, 3, 5, 8, 12…?
The big idea
Look at the gaps between the numbers. The gaps tell you the rule.
Picture it
A staircase: measure each step and you'll know how high the next one is.
Key words
- term
- one number in the series
- gap
- the difference between two neighbouring terms
- rule
- what you do to get from each term to the next
- two series
- two patterns taking turns
Worked examples
- 1Warm-up
3, 7, 11, 15, ?
- Every gap is +4.
- 15 + 4 = 19
- 211+ standard
2, 3, 5, 8, 12, ?
- The gaps grow: +1, +2, +3, +4
- Next gap +5: 12 + 5 = 17
- 311+ standard
4, 20, 6, 18, 8, 16, ?
- Two series take turns.
- 4, 6, 8 go up by 2; 20, 18, 16 go down by 2.
- Next belongs to the first: 10
- 411+ standard
1, 4, 9, 16, ?
- Gaps: +3, +5, +7, so the next gap is +9.
- They're square numbers too: 5 × 5 = 25
The common mistake
The mistake
Every series adds the same number each time.
Instead
Check the gaps; if they change, look at how the gaps change, then try times, then two series.
Why: 11+ series often have growing gaps, multiply, or hide two patterns taking turns.
Where it comes up in the 11+
Number series appear in GL verbal reasoning and in CEM-style numerical reasoning, often with growing gaps or two series.
The video
Video coming soon
We're making a short video that explains number series step by step. Until then, everything it covers is on this page.
Free printable
Number series worksheet
Practice questions on this topic to print and try on paper, at home or on the way to school.
Download the worksheet (PDF)Free account needed: it takes a minute.
Quick quiz
Have a go first, then tap to see the answer.
1. 50, 45, 40, 35, ?
- 30
- 25
- 34
- 31
Show the answerHide the answer
30
Each gap is 5 down.
2. 1, 2, 4, 8, ?
- 16
- 10
- 12
- 14
Show the answerHide the answer
16
Each number doubles: 8 × 2 = 16.
3. 10, 1, 9, 2, 8, 3, ?
- 7
- 4
- 6
- 5
Show the answerHide the answer
7
Two series: 10, 9, 8, 7 and 1, 2, 3.