In this module, you will learn to solve number sequences by identifying the underlying rule in a series of numbers. A number sequence always follows a pattern, such as addition, subtraction, multiplication, division, skipping, combinations of operations, or multi-layered sequences. By carefully analyzing these patterns, you’ll discover which operation is being applied and which number logically comes next in the sequence.
Free practice test
Practice Number sequences for free
Free Number Sequences
12 questions · 5 min
Click the button below to start the test. The timer starts immediately after.
What is a number sequence test?
A number sequence is a row of numbers that follows a fixed rule. You find the rule and fill in the missing number. Number sequences are a standard part of many aptitude tests, because they show how well you spot patterns and reason with numbers.
You often get less than a minute per sequence. Our free practice test has 12 sequences in 5 minutes. Most of the time goes not on arithmetic but on finding the right rule, and that search is something you can practise.
Also called number series, numerical sequences or series completion.
How to solve a number sequence
- Start with the differences between consecutive numbers. If they are equal or grow steadily, you usually have the rule.
- Do the numbers grow fast? Look at multiplying or dividing (×2, ×3, ÷2).
- Do the differences alternate? Split the sequence in two: the numbers in odd and even positions often form separate sequences.
- If nothing else fits, add the two previous numbers (as in Fibonacci).
- Still no rule? Check for squares (1, 4, 9, 16) or prime numbers (2, 3, 5, 7, 11).
- Always check your answer against the whole sequence, not just the last two numbers.
Worked examples
3 – 6 – 12 – 24 – ?
Show answer
48
Each number is the previous one times 2.
2 – 5 – 11 – 23 – ?
Show answer
47
Each number is the previous one times 2, plus 1 (the differences 3, 6, 12 double too).
4 – 9 – 7 – 12 – 10 – ?
Show answer
15
Alternately +5 and −2.
1 – 1 – 2 – 3 – 5 – 8 – ?
Show answer
13
Each number is the sum of the two before it.
1 – 4 – 9 – 16 – 25 – ?
Show answer
36
The squares: 1², 2², 3², 4², 5², so 6² = 36. The differences (3, 5, 7, 9) also grow by 2 each time.
2 – 3 – 5 – 7 – 11 – ?
Show answer
13
The prime numbers: numbers you can only divide by 1 and by themselves. After 11 comes 13.
Practise more with the practice pack
7 practice sets with 106 questions in total, each with an explanation. From €4.99 for 1 day, paid once.
Frequently asked questions
How do I get faster at number sequences?
Check the patterns in the same order every time: differences, multiplication, alternating, adding, squares and primes. Then you never have to work out where to start.
How much time do you get per sequence?
It varies by test. Our free practice test gives you 5 minutes for 12 sequences, so 25 seconds each. If you are stuck, move on. In most tests every question counts equally.
Can I use a calculator?
Usually not for number sequences, and you rarely need one. The numbers are chosen so that you can see the pattern in your head.
Can I practise number sequences for free?
Yes. On this page you practise 12 number sequences for free, with an explanation for every answer. You don't need an account. The practice pack adds more practice sets and a mock test.