Numerical aptitude · Numbers
Number series, made easy
💡 The idea
Every series hides a rule. Almost always you find it by looking at the gaps between the numbers.
2→+3→5→+3→8→+3→11
🧭 The method: 3 steps
- Write the gap between each pair of numbers.
- Same gap → add it. Gaps growing → look at the gaps of the gaps. Numbers growing fast → try × or squares.
- Still stuck? Look at every OTHER number: two patterns may take turns.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
Loading the pictures…
✏️ Worked examples
Example 1. 3, 7, 13, 21, 31, ?
- Gaps: 4, 6, 8, 10
- The gaps go up by 2 → next gap 12
- 31 + 12 = 43
Example 2. 2, 6, 18, 54, ?
- Each is × 3
- 54 × 3 = 162
Example 3. 1, 10, 3, 9, 5, 8, ?
- Odd places: 1, 3, 5 (+2)
- Even places: 10, 9, 8 (−1)
- Next is an odd place: 7
⚠️ Where people go wrong
- Stopping at the first gap: check the gaps of the gaps too.
- Big jumps usually mean multiply or squares, not adding.
📌 Remember
- Gaps first
- Gaps of gaps
- Try ×2, ×3
- Squares 1, 4, 9, 16…
- Every other number