Number Sequence Test

Find the rule in each number sequence and type the next number. Ten questions run from simple steps to squares and Fibonacci, and every answer is explained.

10 questions · about 4 minutes

Question 1 of 10

Difficulty 1 of 5

What comes next?

2468?

Seven common number series types

Almost every sequence question uses one of these rules, or two of them combined.

  1. 01

    Constant difference

    4, 9, 14, 19, 24

    Add or subtract the same number each time. Here the step is +5.
  2. 02

    Constant ratio

    2, 6, 18, 54, 162

    Multiply or divide by the same number each time. Here the step is ×3.
  3. 03

    Alternating rule

    5, 10, 8, 16, 14

    Two operations take turns. Here it is double, then subtract 2, then repeat.
  4. 04

    Interleaved series

    1, 10, 2, 20, 3, 30

    Two separate sequences are woven together. Read every other number to see each one.
  5. 05

    Squares and cubes

    1, 4, 9, 16, 25 and 1, 8, 27, 64

    Perfect squares (1, 4, 9, 16, 25, 36, 49) and cubes (1, 8, 27, 64, 125). Learn them and they show up fast.
  6. 06

    Fibonacci-style

    1, 1, 2, 3, 5, 8, 13

    Each number is the sum of the two before it. Variants start with other numbers, such as 2, 3, 5, 8.
  7. 07

    Changing differences

    3, 6, 11, 18, 27

    The differences are not constant, but their own pattern is: 3, 5, 7, 9. This is called a second-order difference.

A 4-step method for finding the rule

  1. Write the differences. Subtract each number from the next. If they match, you have a constant difference.
  2. Check the ratios. Divide each number by the one before. If they match, you have a constant ratio.
  3. Look at the differences of the differences, or at every other number. A pattern in the gaps means changing differences. Two separate patterns in alternate places means an interleaved series.
  4. Compare with known sets and test the rule. Think of squares, cubes and sums of earlier terms. Then check your rule against every number, not just the last two.

Number series and number sequence mean the same thing in most tests. In strict maths, a sequence is the list and a series is its sum.

For job aptitude tests

Employers often use number series questions in numerical reasoning tests and in hiring tests such as the CCAT and the Wonderlic. They are usually timed, so a method matters more than flair. You can try them under real timing in a free CCAT practice test.

  • Always write the differences down before you guess.
  • Learn squares to 15 and cubes to 10.
  • If a question stalls you for more than a minute, skip it and come back.
  • Check your rule against all the numbers before you answer.

Number patterns are one kind of reasoning. For the visual version, see how to solve matrix IQ questions.

Number sequences and inductive reasoning

A sequence question asks you to infer a rule from a few examples and use it to predict what comes next. That is inductive reasoning. Intelligence tests use it because you have to find the rule with no instructions, so it depends less on what you have been taught.

It also draws on working memory, because you hold the numbers in mind while you test ideas. Practice with the common pattern types helps you spot them faster.

Frequently asked questions

What is a number sequence test?

A number sequence test shows a short list of numbers that follow a hidden rule. You work out the rule and give the next number. Tests like this are common in IQ tests, school entrance tests and job aptitude tests.

What types of number sequences are common?

The most common are constant difference, constant ratio, alternating rules, interleaved series, squares and cubes, Fibonacci-style sums and changing differences. Harder questions combine two rules, such as doubling and adding one.

What is the difference between a number series and a number sequence?

In everyday test language they mean the same thing: an ordered list of numbers with a rule. In strict maths, a sequence is the list and a series is the sum of its terms. Aptitude tests usually say "number series" and mean the list.

How do I find the rule quickly?

Check the differences first. If they are not constant, check the ratios. If neither works, look at every other number, then compare the numbers with squares, cubes and sums of earlier terms.

Why does a number sequence test relate to IQ?

It asks you to infer a rule from examples, which is called inductive reasoning. Reasoning of this kind is part of what many IQ tests measure. This 10-question set is practice and is not an IQ test.

Does practice help with number series questions?

Yes. Knowing the common patterns and the squares and cubes up to about 15 saves time. Practice helps you recognise the pattern types faster. It will not change the reasoning ability underneath.

Are the answers explained?

Yes. After each question you see the rule and the pattern type. At the end you see which pattern types you missed, with the full rule for every question.

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