Number series test: how to find the rule
In a number series test you find the rule behind a row of numbers and pick what comes next. Here are the rules you are most likely to see, worked examples and a free test.
By Shayan Parsai, test developer
Updated
A number series test shows a row of numbers with a gap at the end. You work out the rule that connects them and choose the numbers that come next. It looks like math, but the arithmetic is simple. The skill is spotting the pattern fast, which puts it closer to inductive reasoning than to calculation.
How a number series task works
In our version you see four to six numbers followed by two empty boxes. You choose two numbers from five options and place them in the right order. All the numbers are whole numbers between 0 and 500, so you never need decimals or negative numbers. The series get harder as you go, from simple steps to rules that combine two operations.
Other number sequence tests ask for a single missing number, sometimes in the middle of the row. The method is the same.
Start with the differences
First, check the difference between neighboring numbers. Write the differences under the series. If they are all equal, or two differences take turns, you have the rule.
- 7, 11, 15, 19, 23 goes up by 4 each time, so the next numbers are 27 and 31.
- 3, 5, 10, 12, 17, 19 alternates between +2 and +5, so 24 and 26 come next.
If the differences are not equal, look at the differences themselves. They often form a pattern of their own.
- 2, 3, 5, 8, 12, 17 has the differences 1, 2, 3, 4 and 5. Add 6 and then 7 to get 23 and 30.
- 3, 4, 6, 10, 18 has differences that double: 1, 2, 4 and 8. The next steps are 16 and 32, which gives 34 and 66.
Multiplication and division
When the numbers grow quickly, try multiplying. When they shrink in big steps, try dividing.
- 3, 6, 12, 24, 48 doubles each time, so 96 and 192 come next.
- 320, 160, 80, 40 halves each time, which gives 20 and 10.
Rules that combine two operations are harder. In 4, 9, 19, 39, 79, each number is doubled and then 1 is added, so the next numbers are 159 and 319. If doubling alone almost fits but every number is a little off, look for a constant that is added or subtracted after the multiplication.
Interleaved and alternating series
Sometimes two series are woven together. Read every other number as its own series.
- In 5, 20, 7, 18, 9, 16 the first, third and fifth numbers rise by 2 and the others fall by 2. Next come 11 and 14.
The operation itself can also alternate, for example times 2, plus 3, times 2, plus 3.
- 2, 4, 7, 14, 17, 34 continues with 37 and then 74.
Squares and sums
Two more rules show up at the hard end.
- Square numbers: 4, 9, 16, 25, 36 are 2 × 2, 3 × 3 and so on, so 49 and 64 come next. Sometimes a constant is added. In 5, 10, 17, 26, 37 each number is a square plus 1, which gives 50 and 65.
- The sum of the two numbers before: in 2, 3, 5, 8, 13, 21 each number is the sum of the previous two, so the series continues with 34 and 55.
A checklist for each series
With 45 seconds per series in our test, it pays to check the rules in a fixed order:
- Equal differences, or two differences that take turns.
- Differences that grow by a fixed amount or double.
- Multiplication or division, possibly followed by adding or subtracting.
- Every other number as a separate series.
- Square numbers, or the sum of the two numbers before.
When you think you have the rule, test it on every number in the row, not only the last two. The wrong options in our tasks are the numbers you get from a rule that almost fits: a difference that is a little off, a forgotten step, one step too many, or the right two numbers in the wrong order.
How to practice number series
Practice is mostly about recognizing the rules above without trying ideas at random. Do a set of series against the clock, then read the explanation for each one you missed and note which rule it used. If the same rule keeps catching you, start your next session there.
Our free number series test has 12 series that get harder: four easy, four medium and four hard, with 45 seconds for each. You choose the next two numbers, and after the test you see the rule behind every series. You get new series every time and need no account.
If you are preparing for a test with tables and charts, read the guide to the numerical reasoning test. Finding a rule from a few examples is also the core of an inductive reasoning test.
Frequently asked questions
What is a number series test?
A test where you see a row of numbers and work out which numbers come next. Each series follows a rule, such as adding the same amount, doubling or alternating two steps.
Is a number sequence test the same as a number series test?
Yes, both names describe a row of numbers that follows a rule. Some versions ask for the next numbers, others for a missing number in the middle of the row.
How do you solve number series quickly?
Start with the differences between neighboring numbers. If they do not help, try multiplication, every other number and square numbers, in that order.
Is there a free number series test?
Yes. Ours has 12 series that get harder, with 45 seconds per series and an explanation for every answer. It is free and needs no account.
Try 12 number series
From steady steps to squares and combined rules, with the rule explained for every series. No account needed.