Number Series: Spot the Hidden Rule in Seconds
Crack SSC-CGL number series questions by learning the common patterns - differences, ratios, squares, and mixed rules - with a reliable step-by-step detective method.
By the PadhoDost Team · 📖 6 min read · Updated 4 August 2026
Part of SSC CGL & Banking prep🧠 Be a code-breaker, not a calculator
A number series is like a secret handshake between the numbers. Each term whispers to the next using a fixed rule - add this, multiply that, jump by squares. Your job is not to compute wildly but to eavesdrop: watch how one number turns into the next, catch the pattern, then predict the missing member. Once you find the rule, the answer is almost automatic.
In the General Intelligence & Reasoning section, number series questions test whether you can detect the logic linking a row of numbers and extend it. There is no formula to memorise - just a small family of common patterns and a disciplined way to hunt for them.
The common patterns to check
| Pattern type | How to spot it | Example |
|---|---|---|
| Constant difference | Same number added each time | 3, 7, 11, 15 (+4) |
| Growing difference | Gaps themselves form a pattern | 2, 4, 7, 11 (+2,+3,+4) |
| Constant ratio | Each term multiplied by a fixed number | 3, 6, 12, 24 (x2) |
| Squares / cubes | Terms near n^2 or n^3 | 1, 4, 9, 16 (1^2,2^2,3^2,4^2) |
| Mixed (x then +) | Two operations alternate | 2, 5, 11, 23 (x2 +1) |
| Alternating series | Two series interleaved | 1, 10, 2, 20, 3, 30 |
The detective method
- 1First, find the difference between consecutive terms - is it constant?
- 2If differences grow, check whether THEY form a series (second-level differences).
- 3If differences swing wildly, try ratios instead - divide each term by the previous.
- 4Compare terms to nearby squares and cubes (1,4,9,16,25 and 1,8,27,64).
- 5If nothing fits, suspect two interleaved series - read alternate terms separately.
- 6Confirm your rule works for EVERY gap, not just the first one, before answering.
📝 Worked example: the growing-gap series
Series: 2, 6, 12, 20, 30, ?
Differences: 6-2=4, 12-6=6, 20-12=8, 30-20=10.
The gaps are 4, 6, 8, 10 - increasing by 2 each time.
So the next gap must be 12.
Next term = 30 + 12 = 42.
Bonus insight: these are n(n+1) values - 1x2, 2x3, 3x4, 4x5, 5x6 = 30, then 6x7 = 42.
📝 Worked example: the mixed-operation series
Series: 3, 7, 15, 31, ?
Try x2 then +1: 3x2+1 = 7, 7x2+1 = 15, 15x2+1 = 31. It fits.
So next = 31x2+1 = 63.
Whenever numbers roughly double but not exactly, test 'multiply then add a small constant'.
Quick recall
- ✓Check in order: differences, then ratios, then squares/cubes, then interleaved.
- ✓Second-level differences reveal 'gap-growing' series like 2, 6, 12, 20.
- ✓Memorise squares to 15^2 and cubes to 10^3 - they show up constantly.
- ✓Mixed 'multiply then add' patterns explain near-doubling series like 3, 7, 15, 31.
- ✓A correct rule works for every consecutive pair, not just one.
⚡ Quick check
Find the next term: 4, 9, 19, 39, ?
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