Practise number sequences: Vienna Informatics entrance test
Number sequences (called "Zahlenfolgen" in German too) are part of the cognitive block of the Informatics entrance test at TU Wien and Uni Wien. You get a row of numbers and have to find the rule behind them to fill in the next one. No prior knowledge is needed, just a method and speed.
This page walks through the most common patterns with worked examples and explains one scoring detail that many people miss. Afterwards you can drill number sequences on VWUPass for free, no sign-up required.
Practise number sequences freeWhat number sequences ask of you
A number sequence is a list of numbers that follows a hidden rule. Your job is to spot that rule and give the missing or next number. Almost every sequence can be cracked by asking how you get from one number to the next.
Your first reflex should always be to take the differences between neighbouring numbers. If the numbers rise slowly and evenly, it is usually addition. If they jump sharply, multiplication is often behind it. If they swing back and forth, two sequences are probably interleaved.
- Take differences: this exposes addition and subtraction at once.
- Check ratios: divide each number by the previous one to reveal multiplication.
- Watch the rhythm: irregular jumps hint at two interleaved sequences.
- Add neighbours: if a number equals the sum of the two before it, it is a Fibonacci pattern.
The most common patterns
Most sequences in the entrance test rest on a handful of basic patterns. Recognising them reliably saves precious seconds on every item.
Combined patterns are the most common trap: several operations follow one another, for example first add then multiply, or a step whose size itself keeps growing. If you only look for a single constant difference, you will miss these sequences.
- Arithmetic: constant difference, e.g. 3, 7, 11, 15 (each plus 4).
- Geometric: constant factor, e.g. 2, 6, 18, 54 (each times 3).
- Fibonacci-like: each number is the sum of the two before it, e.g. 2, 3, 5, 8, 13.
- Alternating or interleaved: two sequences taking turns, e.g. 1, 10, 2, 20, 3, 30.
- Combined: several operations, e.g. plus 2 then times 2, or growing steps.
Continue: 3, 6, 12, 24, 48, ?
- First take the differences: 3, 6, 12, 24. They are not constant, so it is not plain addition.
- Check the ratios instead: 6 divided by 3 is 2, 12 divided by 6 is 2, 24 divided by 12 is 2.
- The factor is a constant 2, so this is a geometric sequence (each number is doubled).
- Double the last number: 48 times 2 is 96.
Answer:96
Untangling interleaved sequences
When the numbers seem to jump up and down at random, there is usually no single rule but two sequences written alternately. The trick: look at every second number on its own.
Split the positions into odd (first, third, fifth number) and even (second, fourth, sixth number). Each of these sub-sequences is often cleanly arithmetic or geometric on its own, even when the whole row looks chaotic.
Continue: 2, 100, 4, 90, 6, 80, ?
- The numbers alternate between small and large, which points to two interleaved sequences.
- Take positions 1, 3, 5: those are 2, 4, 6. This sub-sequence rises by 2 each time.
- Take positions 2, 4, 6: those are 100, 90, 80. This sub-sequence falls by 10 each time.
- The seventh position is asked for, i.e. the next number of the first sub-sequence: after 6 comes 8.
Answer:8
The scoring: marking digits correctly
In the entrance test it is not enough to have the number in your head. The answer is marked digit by digit on the answer sheet: for each place of your answer you tick the matching digit in a column. So the arithmetic is only half the job, transferring it cleanly is the other half.
There is one detail that surprises many: if the same digit appears more than once in your answer, it is usually marked only once. For an answer like 88 or 121 you do not tick the repeated digit twice. That is exactly why it pays to practise not just the arithmetic but also the marking in the correct format, so that no points are lost to a formality on test day.
Frequently asked questions
What is the fastest way to spot the pattern in a number sequence?
First take the differences between neighbouring numbers. If they are constant, it is an arithmetic sequence. If not, check the ratios (division) for a constant factor, which means a geometric sequence. If the numbers jump around, look at every second number on its own.
What tricks help with harder number sequences?
Watch for combined patterns: sometimes a multiplication follows an addition, or the step itself grows from number to number. Also test whether a number is the sum of the two before it (Fibonacci pattern) and whether two sequences are interleaved alternately. The rule is usually simpler than it first looks.
Why is a repeated digit only marked once?
Because the answer is marked digit by digit on the answer sheet, and in the test a digit that appears more than once is usually ticked only once. For answers like 88 or 121 you should not mark the repeat twice. Practise the marking in the correct format so you do not lose points to a formality.
Are "Zahlenreihen" and "Zahlenfolgen" the same thing?
Yes, in the context of the entrance test the terms are used interchangeably. In both cases you find the rule behind a series of numbers and supply the next one. In the trainer these tasks appear under the name Zahlenfolgen.
How many number sequences appear in the entrance test?
Number sequences are one of several task types in the cognitive part, alongside syllogisms, word analogies and matrices. The exact count can vary from year to year, so we deliberately do not give a fixed number here. Since the cognitive part is around half the score and pure practice, training pays off especially well here.