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Number series questions: five patterns that solve most of them

A row of numbers and a question mark. Most series on hiring and aptitude tests follow one of five patterns, and checking them in the right order takes seconds. Here they are, with nine examples to try.

Updated October 14, 2026 · by TimedPrep. The 9 examples are practice questions written by us; tap an answer to check yourself.

A number series question shows a few numbers and asks for the next one. It appears on the Wonderlic, the CCAT, the PI Cognitive Assessment and most general aptitude tests. The arithmetic is never hard; the time goes into finding the rule. So the skill is a fixed checking order, not cleverness.

The checking order: (1) differences between neighbors; (2) if the differences are not constant, the differences of the differences; (3) ratios, when the numbers grow fast; (4) every other number, when they jump up and down; (5) squares, cubes and "add the two before". Every series in our question bank follows a rule from one of these five groups.

1. The same step every time

Subtract each number from the next. If the difference never changes, add it once more. The step can be negative or a decimal. Checking takes about three seconds, so always try it first.

Sample · Number series · by TimedPrep

What number comes next in the series? 3, 16, 29, 42, 55, ?

  1. 64
  2. 68
  3. 69
  4. 74
  5. 81

Answer: B. Each number goes up by 13. 55 + 13 = 68. Fast method: check the first two gaps; if they match, apply the same gap once more.

Sample · Number series · by TimedPrep

What number comes next in the series? 9, 22, 35, 48, 61, ?

  1. 72
  2. 73
  3. 74
  4. 75
  5. 87

Answer: C. Each number goes up by 13. 61 + 13 = 74. Fast method: check the first two gaps; if they match, apply the same gap once more.

2. The step itself grows

When the differences are not equal, write them in a row under the series: they usually form their own simple series (+2, +4, +6, ...). Find its next step and add it to the last number.

Sample · Number series · by TimedPrep

What number comes next in the series? 6, 10, 15, 21, 28, 36, ?

  1. 37
  2. 39
  3. 43
  4. 44
  5. 45

Answer: E. Look at the gaps: +4, +5, +6, +7, +8. The gap changes by 1 each time, so the next gap is +9: 36 + 9 = 45. Fast method: write the gaps under the numbers; the pattern is in the gaps.

Sample · Number series · by TimedPrep

What number comes next in the series? 9, 13, 18, 24, 31, 39, ?

  1. 46
  2. 48
  3. 50
  4. 51
  5. 52

Answer: B. Look at the gaps: +4, +5, +6, +7, +8. The gap changes by 1 each time, so the next gap is +9: 39 + 9 = 48. Fast method: write the gaps under the numbers; the pattern is in the gaps.

3. Multiply instead of add

If the numbers double or triple quickly, divide each by the one before. A constant ratio (x2, x3, or /2) is the rule. Big jumps are the signal: a series that reaches the hundreds in five steps is rarely adding.

Sample · Number series · by TimedPrep

What number comes next in the series? 2, 10, 50, 250, ?

  1. 450
  2. 1220
  3. 1230
  4. 1250
  5. 1270

Answer: D. Each number is multiplied by 5. 250 × 5 = 1250. Fast method: when the gaps keep growing, test a ratio (second ÷ first) before anything else.

4. Two series woven together

When the numbers go up and down, read every other number: the 1st, 3rd, 5th form one series and the 2nd, 4th, 6th another. A close relative alternates two steps (+5, -2, +5, -2). Ask which of the two series the missing number belongs to before you calculate.

Sample · Number series · by TimedPrep

What number comes next in the series? 4, 24, 8, 21, 12, 18, ?

  1. 12
  2. 13
  3. 15
  4. 16
  5. 17

Answer: D. Two series are woven together. The 1st, 3rd, 5th terms change by +4 each time, so the next term is 12 + 4 = 16. Fast method: when the numbers jump up and down, read every other term.

Sample · Number series · by TimedPrep

What number comes next in the series? 11, 9, 16, 14, 21, 19, ?

  1. 17
  2. 20
  3. 24
  4. 25
  5. 26

Answer: E. Two steps take turns: −2, then +7. The last step shown was −2, so the next is +7: 19 + 7 = 26. Fast method: when the gaps flip between two values, just continue the rhythm.

5. Squares, cubes and "add the two before"

If nothing above works, test the famous sequences: squares (1, 4, 9, 16), cubes (1, 8, 27) and series where each number is the sum of the two before it. They are rare, which is why they come last.

Sample · Number series · by TimedPrep

What number comes next in the series? 1, 4, 9, 16, 25, ?

  1. 35
  2. 36
  3. 37
  4. 42
  5. 44

Answer: B. These are consecutive squares: the next base is 6, and 6 × 6 = 36. Fast method: memorize squares to 15 and cubes to 6; numbers 1 or 2 away from them are a giveaway.

Sample · Number series · by TimedPrep

What number comes next in the series? 5, 5, 10, 15, 25, 40, ?

  1. 55
  2. 56
  3. 63
  4. 64
  5. 65

Answer: E. Each number is the sum of the two before it: 25 + 40 = 65. Fast method: if the gaps repeat the series itself one step behind, add the last two terms.

The timing rule

Hiring tests give you 14.4 seconds a question (Wonderlic, PI) or 18 (CCAT). A same-step series should take under 10 seconds. Give a series at most two passes of the checking order, about 20 seconds; if no rule has appeared by then, pick the most likely answer and move on. A series you skip costs one point; a series you grind on for a minute costs the three or four questions you never reach.

Now try them on the clock. The free general cognitive test mixes number series with the other common question types: 50 questions, 15 minutes, no sign-up. When the clock stops you see which types cost you points.

Start the free test

Tests that use these questions, each with its own free full-length test: Wonderlic · CCAT · PI Cognitive Assessment.

Common questions

How do you solve number series questions quickly?

Use a fixed order: differences between neighbors first, then the differences of the differences, then ratios, then every other number, and only then squares, cubes and sums of the two before. Most series fall to the first two checks.

Which tests have number series questions?

The Wonderlic, the CCAT, the PI Cognitive Assessment and most general aptitude and cognitive ability tests. They are usually multiple choice with four or five options.

Do these questions come from a real test?

No. They are practice questions written by us in the style of hiring tests. Each answer was derived by a separate checker that solves the series by its own rules.

More question types, one worked example each: the Wonderlic, CCAT and PI sample-question pages · all guides.