A number sequence test shows you a short row of numbers built by a hidden rule and asks for the next number, a missing number in the middle, or the one number that breaks the pattern. The items appear as a standalone test in some assessments (for example German cyquest batteries) and as a question type inside broader numerical or general-ability tests from vendors such as TestGorilla, Criteria and Wonderlic. Each item usually takes 20 to 60 seconds. This guide lists the rule types that come up, gives you a six-step method to find any rule quickly, and finishes with 15 original series and worked solutions.
Formats and timings depend on the vendor, the employer and the test version, so check the instructions screen before you start: some tests are multiple choice, some ask you to type the number.
Key facts
- Also called
- Number series test, number pattern test; German: Zahlenreihen
- Publishers
- cyquest, TestGorilla, Criteria CCAT, Wonderlic
- Format
- Next number, missing number, odd one out, sometimes n-th term
- Answer format
- Multiple choice, 4 or 5 options, or free numeric entry
- Time
- Varies by test; 20–40 s per item, up to 1 min when mixed
- Numbers
- Usually whole numbers; some decimals and fractions
- Calculator
- Often not allowed in general-ability tests
- Adaptive
- Some general-ability tests adapt; series blocks usually fixed
The rule types you will meet
Almost every series in employment tests is built from a small set of rules, used alone or combined:
| Rule type | Example | How to spot it |
|---|---|---|
| Constant difference | 12, 19, 26, 33 (+7) | Differences are all equal |
| Constant ratio | 3, 12, 48, 192 (×4) | Each term is a fixed multiple of the last |
| Alternating operations | +5, −2, +5, −2 | The series zig-zags upwards or downwards |
| Cycle of three or four operations | ×2, +6, ÷2, repeat | Big jumps recur every third or fourth step |
| Second-order differences | differences 3, 5, 7, 9 | The differences form their own simple series |
| Interleaved series | odd positions +3, even positions −4 | Two simple series alternate |
| Growing operand | ×1, ×2, ×3 or +1, +2, +4, +8 | One operation stays the same, the number it uses grows |
| Squares, cubes, primes | 4, 9, 16, 25; 2, 3, 5, 7, 11 | Terms are familiar numbers, sometimes ±1 |
| Sum of previous terms | 2, 3, 5, 8, 13 | Each term equals the sum of the two before it |
Harder tests combine two of these, for example an alternating operation where one operand grows, or a cycle that contains a division. If the differences look chaotic, a hidden ×2, ×3 or ÷2 is the usual cause.
How to solve a number sequence in six steps
Work through every series in the same order. A fixed routine is faster than trying ideas at random.
- Write the differences under the series, with signs. If they are constant, rising evenly or repeating, you are done.
- Take the differences of the differences. If that second row is constant, you have a second-order series.
- Check ratios when terms jump by roughly ×2, ×3 or halve. Multiplication and division hide inside many cycles.
- Look for a cycle. Compare step 1 with step 3 and step 4. If the same operation recurs, count where you are in the cycle for the next term.
- Split the series. Read positions 1, 3, 5, 7 and then 2, 4, 6. Two simple series are often interleaved.
- Test the rule on every term, not just the last three. A rule that explains only part of the series is usually wrong.
Two formulas help with "find the 20th term" items, which some tests include:
- Arithmetic (constant difference d, first term a): n-th term = a + (n − 1) × d. Example: 7, 11, 15 … the 20th term is 7 + 19 × 4 = 83.
- Geometric (constant ratio r): n-th term = a × r^(n − 1). Example: 3, 6, 12 … the 8th term is 3 × 2^7 = 384.
Number sequence test practice: 15 original series
All series were written for this guide and checked term by term. Set a timer for 8 minutes (about 30 seconds per item). Items 1–12 ask for the next number; 13 and 14 ask for a missing number; 15 is odd one out.
| No. | Series | Options (if multiple choice) |
|---|---|---|
| 1 | 87, 80, 73, 66, 59, ? | 50 / 52 / 53 / 54 |
| 2 | 5, 9, 7, 11, 9, 13, ? | 11 / 15 / 12 / 17 |
| 3 | 2, 6, 18, 54, ? | 108 / 72 / 162 / 216 |
| 4 | 3, 5, 9, 15, 23, 33, ? | 43 / 45 / 47 / 44 |
| 5 | 4, 30, 7, 27, 10, 24, 13, ? | 16 / 21 / 22 / 20 |
| 6 | 5, 10, 7, 14, 11, 22, ? | 19 / 44 / 25 / 17 |
| 7 | 2, 5, 10, 17, 26, 37, ? | 48 / 49 / 50 / 52 |
| 8 | 2, 3, 5, 7, 11, 13, ? | 15 / 16 / 17 / 19 |
| 9 | 1, 4, 5, 9, 14, 23, ? | 32 / 37 / 36 / 41 |
| 10 | 5, 10, 16, 8, 16, 22, 11, ? | 17 / 22 / 5.5 / 28 |
| 11 | 3, 3, 6, 18, 72, ? | 144 / 288 / 360 / 216 |
| 12 | 200, 199, 196, 187, 160, ? | 79 / 133 / 106 / 81 |
| 13 | 6, 11, ?, 30, 44 | free entry |
| 14 | 0.5, 1.5, ?, 13.5, 40.5 | free entry |
| 15 | Which number does not fit? 3, 7, 15, 31, 62, 127 | free choice |
Solutions and worked steps
1. Answer: 52. Constant difference −7: 59 − 7 = 52. The warm-up. If you picked 53 you subtracted 6; write the differences rather than eyeballing them.
2. Answer: 11. Alternating +4, −2: 5 → 9 → 7 → 11 → 9 → 13 → 11. The last step was +4, so the next is −2. The trap option 17 continues +4.
3. Answer: 162. Constant ratio ×3: 54 × 3 = 162. Differences (4, 12, 36) also triple, which is the signature of a geometric series.
4. Answer: 45. Differences: 2, 4, 6, 8, 10. The next difference is 12: 33 + 12 = 45. Second-order series: the differences rise by 2 each time.
5. Answer: 21. Two interleaved series. Odd positions: 4, 7, 10, 13 (+3). Even positions: 30, 27, 24 (−3). The 8th term is an even position: 24 − 3 = 21. Taking differences of the whole series (+26, −23, +20 …) works too, but it is slower.
6. Answer: 19. Alternating ×2 and −3: 5 → 10 → 7 → 14 → 11 → 22 → 19. The last step was ×2, so the next is −3. The trap is 44 (another ×2).
7. Answer: 50. Squares plus one: 1² + 1 = 2, 2² + 1 = 5, 3² + 1 = 10 … 7² + 1 = 50. The differences (3, 5, 7, 9, 11) give the same answer as a second-order series, so both routes work.
8. Answer: 17. Prime numbers in order. The next prime after 13 is 17 (15 = 3 × 5 and 16 are not prime).
9. Answer: 37. Each term is the sum of the two before it: 1 + 4 = 5, 4 + 5 = 9, 5 + 9 = 14, 9 + 14 = 23, 14 + 23 = 37. Suspect this rule when the differences repeat earlier terms of the series (3, 1, 4, 5, 9).
10. Answer: 22. Cycle of three operations: ×2, +6, ÷2. 5 ×2 = 10, +6 = 16, ÷2 = 8, ×2 = 16, +6 = 22, ÷2 = 11, ×2 = 22. The differences (+5, +6, −8, +8, +6, −11) look random; the halving from 16 to 8 gives the cycle away.
11. Answer: 360. Growing multiplier: ×1, ×2, ×3, ×4, then ×5. 72 × 5 = 360. The repeated 3 at the start is the clue that the first multiplier is 1.
12. Answer: 79. Differences: −1, −3, −9, −27. Each difference is three times the last, so the next is −81: 160 − 81 = 79. Option 133 continues −27, a common slip.
13. Answer: 19. Work outwards from the known gaps. 44 − 30 = 14. If the differences rise by 3, they run 5, 8, 11, 14: 6 + 5 = 11, 11 + 8 = 19, 19 + 11 = 30, 30 + 14 = 44. Every term checks.
14. Answer: 4.5. Constant ratio ×3: 0.5 × 3 = 1.5, × 3 = 4.5, × 3 = 13.5, × 3 = 40.5. Decimals do not change the rules.
15. Answer: 62. The rule is "double and add one": 3 → 7 → 15 → 31 → 63 → 127. The fifth term should be 63; 62 breaks the pattern. In odd-one-out items, find the rule from the terms that agree, then test each term against it.
Scoring yourself: 14–15 correct in 8 minutes means you are ready. 10–13 means the rule types are there but speed is not yet; repeat the method on fresh series. Below 10, go back to the six steps and do series untimed until each step is automatic.
Traps and how to avoid them
- Stopping at differences. Many series contain a ×2 or ÷2 in a cycle (items 6 and 10). Check ratios when jumps are large.
- Losing your place in a cycle. Write the operation above each arrow, then count which step comes next.
- The "continue the last step" option. Test writers put the result of repeating the last operation among the options (items 2, 6 and 12). If your answer matches it, double-check the cycle.
- Off-by-one in n-th term items. The first term is term 1, so the 20th term adds 19 differences, not 20.
- Checking only the last few terms. A rule must explain every term.
- Typos in free-entry tests. There are no options to warn you. Read the typed number once against your notes.
- Spending too long. If no rule appears after about 40 seconds, choose the most plausible option and move on. A blank answer scores nothing.
How to prepare
Five days, 30 minutes a day:
| Day | Focus |
|---|---|
| 1 | Learn the rule-type table above. 15 easy series (constant difference, ratio, alternating) untimed |
| 2 | Cycles with × and ÷: 15 series, writing the operation over every arrow |
| 3 | Second-order, interleaved, growing-operand and sum-of-previous series: 15 series |
| 4 | Mixed set of 15 in 8 minutes, then review every error by rule type |
| 5 | A second timed set; target 13 or more correct with a minute to spare |
Number facts that save time: squares up to 20² (400), cubes up to 10³ (1,000), primes up to 50, powers of 2 up to 2¹⁰ (1,024) and powers of 3 up to 3⁶ (729). Recognising 343 as 7³ or 729 as 3⁶ turns a hard item into an easy one.
On the day: have pen and paper ready, use a laptop or desktop rather than a phone if the test allows, and read whether the test is multiple choice or free entry before the first item.
Sources
- cyquest, QualiMatcher product page (module "Fortführen von Jahreszahlen": recognise the rule and apply it to the next financial year): https://talent-assessment.tools/qualimatcher/
- TestGorilla, Numerical Reasoning test (covered skills include number series and patterns; about 10 minutes)
- Criteria Corp, What to expect on the CCAT (50 questions, 15 minutes, no calculators; maths and logic section)
MSc Psychology, 7 years of test taking.
Last updated: Oct 1, 2026