Number sequences appear in puzzles, aptitude tests and casual games. Most of them follow a small set of rules. Once you know what to look for, you can usually narrow the possibilities quickly instead of guessing at random.
This guide covers the patterns you will meet most often: constant addition or subtraction, multiplication, alternating rules, and sequences where the difference itself grows. Each section includes short worked examples.
Constant addition (arithmetic sequences)
The simplest pattern: each term increases (or decreases) by the same amount.
Difference: +5 each time. Next term: 19 + 5 = 24.
When the numbers are larger, still check the first differences before looking for more complex rules.
Constant difference of +15 → next is 165.
Constant subtraction
The same idea in the opposite direction. Confirm the difference is steady rather than growing.
Difference: −7 each step. Next: 29 − 7 = 22.
Multiplication (and occasional division)
Each term is multiplied by a fixed factor (or divided by one).
Multiply by 2 each time → 48.
Divide by 3 → next is 1.
Sometimes the multiplier itself changes in a simple way (×2, ×3, ×4 …). Check whether a single constant factor works first; only then consider a changing factor.
Alternating patterns
Two interleaved rules are common. Odd positions may follow one rule and even positions another, or the sequence may alternate between two operations.
Look at odd terms: 2, 4, 8 … (×2)
Even terms: 5, 9, 17 … (+4, +8 — differences doubling)
A simpler view: alternate “add 3” and “double the previous odd term” style rules. Always test the simplest consistent explanation.
Another frequent style: add then subtract, or multiply then subtract a constant.
Pattern: ×2, −2, ×2, −2, ×2 … → next after 28 is 26.
Increasing (or decreasing) differences
The first differences are not constant; they themselves form a simple sequence (often +1, +2, +3 … or +2, +4, +6 …).
Differences: +1, +2, +3, +4 → next difference +5 → 11 + 5 = 16.
Differences: +2, +4, +8, +16 (powers of 2) → next difference +32 → 65.
Writing the differences underneath the sequence is one of the most reliable habits for these problems.
Worked multi-step example
Differences: +3, +6, +9, +12 → next difference +15
37 + 15 = 52.
The second differences are constant (+3), which confirms the pattern.
Common mistakes
- Stopping at the first plausible rule — check that the rule fits every given term, not only the first two or three.
- Ignoring units or signs — a sequence of negatives or mixed signs needs the same careful difference analysis.
- Over-complicating — try constant difference, then constant multiplier, then alternating or second differences before inventing exotic rules.
- Arithmetic slips when applying the rule — once the pattern is clear, re-compute the next term carefully.
A simple checklist
- Write the sequence clearly and compute successive differences.
- Ask: is the first difference constant?
- If not, is there a constant multiplier?
- Are there two interleaved sequences?
- Do the differences themselves form a simple sequence?
- Verify the candidate rule against all given terms.
Practising with BrainBaazi Number Sequence
The Number Sequence game on BrainBaazi presents progressive levels built around these kinds of patterns. Because each level is short, you can focus on applying the checklist rather than racing for speed at the beginning. Progress is saved locally in your browser.
Open the game from the Online Games page. If you also enjoy arithmetic under light time pressure, the companion article Quick Math Tips covers related calculation habits.
Conclusion
Most number-sequence puzzles yield to a systematic look at differences and simple multipliers. Start simple, write the differences down, and only move to alternating or second-order patterns when the first-level rules fail. With a little deliberate practice the common families become familiar, and solving becomes a matter of recognition rather than guesswork.