Learn the 3-Step Method
1Write the gaps.
3→4→6→9→13: gaps 1, 2, 3, 4. The gaps themselves often form the pattern.
2No sense? Split odd and even positions.
1,10,2,9,3,8 → chain A: 1,2,3 · chain B: 10,9,8. Braided sequences are a VR favourite.
3Know the famous families.
Squares 1,4,9,16,25 · doubles 2,4,8,16,32 · triangular 1,3,6,10,15.
Worked Example
Find the next number: 2, 4, 8, 16, ?
Watch Out! Common Mistakes
Gap the gaps! They grow: +1,+2,+3,+4 → next +5 → 18.
Split alternates! Odd positions climb 1,2,3; even fall 10,9,8. Next (position 7, chain A) = 4.
Famous family! They’re 1², 2², 3², 4² → next is 5² = 25.
⬇ Cheat Sheet
- Write the gaps; look for a gap pattern.
- Nonsense gaps → split into two alternating chains.
- Memorise: squares, doubles, triangular numbers.
- Verify your rule on every given term.
📖 Continue Your Journey
Quick summary
- Write out the gaps — they often form their own pattern.
- Senseless gaps usually mean two interleaved chains: split alternate terms.
- Know the families: squares, doubles, triangular numbers.
- Test the rule against every term before answering.
Frequently asked questions
What are interleaved sequences?
Two simple sequences braided alternately: 1, 10, 2, 9, 3, 8 is 1-2-3 climbing woven with 10-9-8 falling — the next term is 4.
Which special sequences should children memorise?
Square numbers (1, 4, 9, 16, 25), doubling (2, 4, 8, 16, 32) and triangular numbers (1, 3, 6, 10, 15) cover most 11+ surprises.
How is this different from school sequences?
Same maths, sneakier disguises — growing gaps and braids appear more often, and speed matters more.
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