Example 1 · level 1 — a gentle start
A sequence starts 5, 10, 15, 20, … What is term 8?
- 25
- 41
- 45
- 40
Answer: 40 — Term n = first term + 5 × (n − 1).
11+ sequence rules (nth term) questions
Sequence rules (nth term) comes up in the maths paper of every major 11+ format. Here is what the questions look like, the method that works under time pressure, and five worked examples with the full reasoning, from a gentle start to a hard paper.
Maths · examined by GL and CEM · 5 worked examples
What your child needs to know
- Find the jump between the terms first. That number goes in front of the n.
- For 3, 7, 11, 15 the jump is 4, so the rule starts 4n. But 4 × 1 = 4, and the first term is 3.
Where marks get lost: So adjust: the rule is 4n − 1. Always check it against the first term AND a later one.
Worked examples
Every question below is generated by the same engine your child practises on, and every answer is derived by our checker rather than written by hand — which is why we can put them on a public page at all.
Example 2 · level 2 — typical of early practice
A sequence starts 9, 11, 13, 15, … What is term 10?
- 90
- 29
- 17
- 27
Answer: 27 — Term n = first term + 2 × (n − 1).
Example 3 · level 3 — standard paper difficulty
What is the nth-term rule for 11, 16, 21, 26, …?
- 5n − 6
- 5n
- n + 5
- 5n + 6
Answer: 5n + 6 — The numbers go up by 5, so the rule starts 5n; then adjust to hit the first term.
Example 4 · level 4 — a harder paper
What is the nth-term rule for 18, 21, 24, 27, …?
- 3n + 15
- 3n
- n + 3
- 3n − 15
Answer: 3n + 15 — The numbers go up by 3, so the rule starts 3n; then adjust to hit the first term.
Example 5 · level 5 — the level that separates candidates
A sequence starts 21, 31, 41, 51, … What is term 23?
- 251
- 241
- 61
- 483
Answer: 241 — Term n = first term + 10 × (n − 1).
How to practise this at home
- Work in short, frequent sessions. Ten minutes daily beats an hour at the weekend, because the recall gap is what builds memory.
- Insist on written working, even for questions your child can do in their head — under exam pressure the method is what survives.
- When an answer is wrong, ask them to explain their reasoning before you correct it. The error is almost always in one step, not the whole approach.
Practise sequence rules (nth term) with a tutor that explains
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