Number series questions: the 6 patterns and how to spot them fast
A number series question shows a sequence and asks for the next (or missing) number. Almost every series uses one of six patterns: a constant difference, a growing difference, multiplication, squares or cubes, two interleaved series, or adding the previous two terms. Write the differences under the series and most patterns appear in seconds. Number series are common in the CCAT and in placement aptitude tests. For the wider family, see logical reasoning tests.
- Six patterns cover nearly every series.
- Start by writing the differences between terms.
- Growing gaps? Look at the differences of the differences.
- Nothing in the gaps? Try ratios, squares, alternation, sums.
- Aim for 20–30 seconds each; forge's CCAT-style bank has 32 series items.
Free sample question
Number series question
One of the six patterns, with the rule explained.
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Quick summary
- Most number series use one of six patterns.
- Start with the differences between consecutive terms.
- If differences grow, look at the second differences.
- Then check multiplication, squares and cubes, alternation and sums.
- Move on after about 30 seconds if nothing fits.
The six patterns
| Pattern | Example | Next |
|---|---|---|
| Constant difference | 7, 11, 15, 19, 23 | 27 (+4) |
| Growing difference | 3, 4, 6, 9, 13 | 18 (+1, +2, +3, +4, +5) |
| Multiplication | 2, 6, 18, 54 | 162 (×3) |
| Squares (± constant) | 2, 5, 10, 17, 26 | 37 (n² + 1) |
| Two interleaved series | 1, 20, 3, 18, 5, 16 | 7 (odd positions +2) |
| Sum of previous two | 2, 3, 5, 8, 13 | 21 |
Differences: 2, 4, 6, 8. The gaps grow by 2, so the next gap is 10: 24 + 10 = 34.
Two series: 3, 6, 12 (×2) in the odd positions and 30, 27, 24 (−3) in the even positions. The next term is in the odd series: 12 × 2 = 24.
Letter series work the same way
Convert letters to numbers (A = 1, B = 2 … Z = 26) and apply the same checks. B, E, H, K is 2, 5, 8, 11 (+3), so the next letter is 14 = N.
Practise series under time pressure
CCAT-style logic drills with number and letter series, plus free logical reasoning practice on forge.
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Source notes
The series count describes forge's CCAT-style question bank. All examples and game items are written or generated by forge.
Frequently asked questions
How do you solve number series questions?
Work through a fixed checklist: constant difference, growing difference, multiplication, squares or cubes, two interleaved series, and adding the previous two terms. Writing the differences under the series reveals most patterns within seconds.
What are the most common number series patterns?
Adding or subtracting a constant, gaps that grow by a fixed amount, multiplying by a constant, square or cube numbers (sometimes plus or minus a constant), alternating two series, and Fibonacci-style sums.
Which tests include number series questions?
Number series are common in the CCAT, in Indian placement aptitude tests, in some Aon and Talent Q-style logic tests, and in general aptitude screens. They're less common in SHL graduate tests, which use data tables instead.
What if the differences don't show a pattern?
Check ratios between terms, check every second term (two interleaved series), compare each term with square numbers, and see whether each term is the sum of the previous two.
How long should a number series question take?
Aim for 20 to 30 seconds. If none of the six checks reveals a pattern in that time, guess and move on.
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