Practice number sequences for free

There are different types of number sequences:

Basic Number Sequence: A simple sequence in which each number differs by a fixed amount from the previous number.
Variable Sequence: A sequence where the change between numbers varies but follows a constant pattern.
Number Sequence with Double Analysis Layer: A more complex sequence that requires an additional layer of analysis to discover the pattern.
Fractions and Powers: Sequences in which numbers consist of fractions or powers with a regularity in the numerator and/or denominator.
Fibonacci Sequence: A famous sequence in which each number is the sum of the two preceding numbers.
Repeating Pattern: A sequence in which the numbers occur in a specific, repeating pattern.
Skipping Pattern: A sequence in which two different sequences are present, requiring you to skip a number each time to discover the pattern.

Step 1: Practicing Number Sequences: The Basics

When practicing number sequences, it is important to identify the type of sequence. Use pen and paper to easily identify the patterns by writing down the steps between the numbers. The operations +, -, *, /, ^, and square roots can all appear in the different types of sequences.

The basic number sequence

2, 4, 6, 8, 10, 12, ?

The pattern is simple: each number is 2 more than the previous one. The 7th number in the sequence would therefore be 14. It helps to write down the step to the next number on paper each time to quickly recognize the pattern: +2, +2, +2,…

For example, when jumping from 4 to 8, you don’t know if it’s +4 or *2. So always write both options on your scratch paper.

4, 8, 12, 24, 28, 56, ?

Answer: The pattern is *2, +4, *2, +4. So the answer is 60.

This specific example is a sequence with a repeating pattern.

Sequence

20, 19, 17, 14, 10, 5, ?

Here we see a change in the numbers that varies as follows:

-1, -2, -3, -4, -5,….

Then the next change must be -6, and the answer is -1.

Number Sequence with Double Analysis Layer

2, 4, 16, 96, 768, 7680, ?

Here we see the pattern

*2, *4, *6, *8, *10, ?

Where the pattern in the second layer is a constant factor, namely

+2, +2, +2, +2, +2

So we need to multiply 7680 by (10+2) = 12 to get the correct answer. The pattern is therefore

*2, *4, *6, *8, *10, *12

And the answer is 92,160.

Sometimes it’s hard to figure out the pattern in a sequence of numbers. By analyzing the second layer of the pattern, the sequence may turn out to be easier than you first thought.

Fractions and Powers

Fractions and powers can be used both to create separate sequences and to appear as numbers within a sequence themselves. For example, the numerator and denominator can each form their own sequence, or you can work with the result of the fraction or power. An example of fractions forming separate sequences with the numerator and denominator as their own sequences:

1/2, 2/3, 3/4, 4/5, ?/?

Numerator: 1, 2, 3, 4, ?

Denominator: 2, 3, 4, 5, ?

The sequence must then be: 1/2, 2/3, 3/4, 4/5, 5/6

In addition, we can work with the result of a fraction or a power. For example, if we take the powers of 2, we get the sequence:

2^1, 2^2, 2^3, 2^4, ?

This results in the numbers:

2, 4, 8, 16, ?

And then we see that the pattern must be *2 each time. So the answer is 32 or 2^5.

Fibonacci Sequence

A famous sequence in which each number is the sum of the two preceding numbers. An example of a Fibonacci sequence with 6 numbers, where the 7th number is unknown:

2, 3, 5, 8, 13, 21, ?

In this case, the 7th number is the sum of the last two numbers in the sequence:

21 + 13 = 34

The complete sequence up to and including the 7th number is:

2, 3, 5, 8, 13, 21, 34

Variations on the Fibonacci sequence

A Fibonacci sequence in which each number is the sum of the three preceding numbers looks like this:

2, 3, 5, 10, 18, 33, ?

Here you can see that each number is formed by the sum of the three preceding numbers:

2 + 3 + 5 = 10
3 + 5 + 10 = 18
5 + 10 + 18 = 33 And so on.

A sequence in which each number is the sum of all preceding numbers would look like this:

1, 1, 2, 4, 8, 16, 32, ...

In this sequence, each number is the sum of all preceding numbers:

1
1 + 1 = 2
1 + 1 + 2 = 4
1 + 1 + 2 + 4 = 8
1 + 1 + 2 + 4 + 8 = 16
1 + 1 + 2 + 4 + 8 + 16 = 32 And so on.
The answer is then 64.

A Fibonacci sequence using multiplication instead of addition is also possible. Here, each subsequent number is obtained by multiplying the two previous numbers.

1, 2, 2, 4, 8, 32, 256, ?

The pattern is:

1 × 2 = 2
2 × 2 = 4
2 × 4 = 8
4 × 8 = 32
8 × 32 = 256
And so on.

Each time, the two previous numbers are multiplied together to determine the next number. 32 × 256 = 8,192.

Skipping Pattern

This involves two different patterns in the same sequence, requiring you to skip a number to discover the correct pattern. An example is as follows:

3, 2, 11, 4, 19, 8, ?

The first sequence starts at 3 and increases by +8 each time; the second sequence starts at 2 and doubles each time. In this case, only the first sequence is relevant. The next number in the sequence must therefore be 19 + 8 = 27.

Step 2: Practicing number sequences: a step-by-step approach

Since some problems take more time than others, it is helpful to follow a structured approach when solving sequences. Although you never know exactly which underlying principle the sequence follows beforehand, some sequences are easier to solve than others.

The most promising tactic is:

1. First, check whether it is a regular sequence or a repeating sequence.

2. Check for a skipping pattern.

3. Investigate whether it is a Fibonacci sequence.

4. For fractions and powers, check whether they are two separate sequences or a single combined sequence.

By following these steps, you’ll quickly have examined a large portion of the possible patterns without wasting unnecessary time. Practicing number sequences is essential for spotting patterns faster.

Conclusion: Practicing number sequences increases your chances of success

By regularly practicing number sequences, you’ll discover patterns faster and faster. This is important because number sequences are common in assessments from well-known providers such as HARVER, NOA, HFM-VIT, HFM-SIT, LTP, and Cubiks. By practicing our free number sequences, you can improve your skills and confidently take your 21+ exam, HBO or MBO entrance exam, aptitude test, intelligence test, IQ test, or assessment for your job application or selection process.

Practice Number sequences for free

New to Number sequences? Click here for an explanation.

New to Number sequences? Click here for an explanation.