Number sequences questions appear in almost every GL-style verbal-reasoning paper, and they are one of the most rewarding types to master because the same handful of underlying patterns comes up again and again. Your child is shown a numeric series with one term missing or with a gap at the end, and must work out the rule that links the numbers, then apply it. Continue the series 2, 5, 11, 23, … and the moment a child has a fixed, repeatable method, these questions stop being a guessing game and become almost mechanical. This guide gives you that method, a full worked example, the traps that cost marks, and a realistic practice plan.
Where number sequences sit in the 11+
Verbal reasoning is one of the four assessed skill areas in the 11+, alongside English, maths and non-verbal reasoning. Since CEM's separate 11+ tests were largely phased out around 2022-2023, GL Assessment now dominates most selective regions, with bespoke and consortium papers such as the Essex CSSE elsewhere. GL verbal-reasoning papers are multiple-choice, tightly timed at roughly a minute a question, with answers marked A to E on a separate answer sheet and no calculator allowed. Number sequences typically make up three to five questions per paper. Because each carries the same mark as any other question, fast and reliable technique on this predictable type is some of the highest-value preparation available. A strong raw score feeds into an age-adjusted Standard Age Score (SAS, roughly 69-141 with 100 as average), and many grammar schools look for around 111 or above, though exact requirements vary by area and year.
The fixed method
Teach your child to run the same five steps every single time, in order, rather than staring and hoping the answer jumps out:
- Write the gaps. Under each pair of terms, write the difference. This one habit solves the majority of questions instantly.
- Check if the differences are constant. If they are, it is a simple add or subtract rule. Extend it.
- If not, look at how the differences change. Are they doubling, growing by a fixed step, or following their own smaller sequence?
- Test multiply-then-adjust rules. Try ×2, ×2+1, ×2-1, ×3 and similar, because geometric growth is extremely common.
- Suspect two interleaved sequences. If nothing fits, split the series into odd positions (1st, 3rd, 5th) and even positions (2nd, 4th, 6th) and check each separately.
Ninety per cent of 11+ number sequences fall to steps one to three. Steps four and five catch the harder ones that separate a good score from a top score.
The common pattern types
Encourage recognition of these recurring families so your child names the pattern quickly rather than reinventing it each time.
| Pattern type | Example | Rule |
|---|---|---|
| Constant difference | 4, 7, 10, 13 | Add 3 each time |
| Increasing difference | 1, 2, 4, 7, 11 | Add 1, then 2, then 3… |
| Doubling difference | 2, 5, 11, 23 | Differences double (3, 6, 12…) |
| Multiply and adjust | 1, 3, 7, 15 | ×2 then +1 |
| Interleaved | 2, 9, 4, 7, 6, 5 | Two series woven together |
| Squares or related | 1, 4, 9, 16 | Square numbers |
Worked example, step by step
Take the series 2, 5, 11, 23, and find the next term. First, write the differences underneath: from 2 to 5 is 3, from 5 to 11 is 6, from 11 to 23 is 12. The differences are 3, 6, 12 — each one is double the last. So the next difference should be 24. Add that to the final term: 23 + 24 = 47. The answer is 47. Notice how the second layer of differences unlocked it: a child who only looked at the surface numbers would flounder, but a child who wrote the gaps saw the doubling instantly. That is why step one is never optional.
A harder interleaved example
Consider 3, 20, 6, 17, 9, 14, and find the next term. The differences jump around wildly (+17, -14, +11…), which is your signal to split. Odd positions are 3, 6, 9 — increasing by 3. Even positions are 20, 17, 14 — decreasing by 3. The next term continues the odd sequence, so after 14 comes 12. Whenever the differences look chaotic, do not abandon the question; split it into two woven series and the calm pattern usually appears.
The traps that cost marks
- Stopping at the first pattern that fits two terms. A rule must fit every gap, not just the first pair. Always test it against the whole series before committing.
- Forgetting to check interleaved series. If a difference pattern looks random, split odd and even positions before giving up.
- Answer-sheet slips. On a GL paper the answer goes in a separate lettered box. A correct working, marked in the wrong row, scores zero — teach steady bubbling.
- Arithmetic errors under time pressure. A single miscalculated difference derails the whole series, so a quick recheck of the gaps pays off.
- Ignoring subtraction and decimals. Sequences can go down as well as up, and occasionally step in halves or tenths.
How to practise this type
Little and often wins: five questions of this type daily for a week beats fifty crammed into one sitting, because pattern recognition is a habit that builds through spaced repetition. Our free verbal-reasoning worksheets are organised by exact question type, so your child can drill number sequences in isolation until the method is automatic. The Arena's VR mode gives instant feedback with XP and a spot on the live leaderboard to keep motivation high. Once the type feels effortless, fold it back into full timed mock papers so pacing develops alongside accuracy, and use the revision hub to track which VR types still need work. For the full picture of what else the paper contains, see the 21 VR types overview, and check the key 11+ dates so your timeline stays on track.
Frequently asked questions
Is a calculator allowed for these questions?
No. GL verbal-reasoning papers are done entirely without a calculator, so mental arithmetic and quick difference-spotting are essential. This is one reason strong number-bond fluency helps enormously.
How many number sequences will my child face?
Usually three to five per verbal-reasoning paper, though the exact count varies by region and year. Because they are so predictable in style, they are among the most reliable marks to secure with practice.
What if my child cannot spot the rule at all?
Teach them to move on and return later rather than burning a full minute stuck. In a timed paper, banking the easy questions first and coming back to a tricky sequence protects the overall score far better than freezing on one item.