11+ Maths · Topic explained
Sequences
What comes next: 3, 7, 11, 15…? And what's the 50th number?
The big idea
A sequence follows a rule: find the jump between terms and you've cracked it.
Picture it
Like stepping stones evenly spaced: know the size of each step, and you can keep going.
Key words
- term
- One number in a sequence.
- term-to-term rule
- How to get from one term to the next: '+4'.
- nth term
- A rule that gives any term from its position, like 4n − 1.
- position
- Where a term is: 1st, 2nd, 3rd…
Worked examples
- 1Warm-up
What comes next: 5, 8, 11, 14, ?
- The jump is +3 each time
- 14 + 3 = 17
- 211+ standard
What comes next: 40, 33, 26, 19, ?
- The jump is −7 each time
- 19 − 7 = 12
- 311+ standard
What comes next: 2, 3, 5, 8, 12, ?
- The jumps grow: +1, +2, +3, +4
- Next jump +5: 12 + 5 = 17
- 411+ standard
Find the nth term of 4, 7, 10, 13… and the 20th term
- Jump +3, so start with 3n: 3, 6, 9, 12
- Each term is 1 more: 3n + 1
- 20th term: 3 × 20 + 1 = 61
The common mistake
The mistake
In 3, 7, 11, 15… the 10th term is 10 × 4 = 40.
Instead
The rule is 4n − 1, so the 10th term is 40 − 1 = 39.
Why: The jump tells you the times table (4n); then check how far each term is from it.
Where it comes up in the 11+
Next-term and missing-term questions, growing patterns of shapes, and the nth term in harder papers.
The video
Video coming soon
We're making a short video that explains sequences step by step. Until then, everything it covers is on this page.
Free printable
Sequences 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. What comes next: 6, 11, 16, 21, ?
- 25
- 26
- 27
- 31
Show the answerHide the answer
26
The jump is +5: 21 + 5 = 26.
2. What comes next: 1, 4, 9, 16, ?
- 20
- 23
- 25
- 32
Show the answerHide the answer
25
They're square numbers: 5 × 5 = 25.
3. A sequence has nth term 5n − 2. What is the 10th term?
- 30
- 48
- 50
- 52
Show the answerHide the answer
48
5 × 10 − 2 = 48.