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Maths Olympiad · topic 2 of 33 · free

Number patterns: what comes next? — Maths Olympiad practice

A number series hides a rule. Write the gap between each pair of neighbours: the same gap every time, a gap that grows, gaps that take turns, or numbers that are doubled. Once you see the rule, the next number is easy.

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How to solve it

Look at the gaps — “write the jump between each pair of numbers — the jumps show the rule”

  1. Write the gap between each pair of neighbours (+4, +4, … or −3, −3, …).
  2. Same gap? Add it again. Growing gap (+2, +3, +4)? The next gap is one more.
  3. Gaps that take turns (+5, −2, +5, −2)? Use the next one in turn. Numbers growing fast? Try × 2 or × 3.

Use it for: “What comes next”, “find the missing term” and pattern questions in every Olympiad paper.

Worked example: What comes next? 3, 5, 8, 12, 17, ? → 23

  1. The gaps are +2, +3, +4, +5 — each gap is one more than the last.
  2. The next gap is +6: 17 + 6 = 23.

Check: 3, 5, 8, 12, 17, 23 has gaps 2, 3, 4, 5, 6 — one rule all the way ✓

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✓ Written and checked by the TalentJR team · Updated 13 Oct 2026 · How we make our lessons

✏️ Practice

Work it out on paper, then tap the answer you think is right. Stuck? Press “Show me how” to see every step.

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🏁 Topic 2 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Number Series Worksheet for Maths Olympiad

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