Number Sequences

Number sequences can be used as a tool to practice and improve your numerical reasoning skills. These types of test are found in IQ Tests, psychometric assessments and aptitude tests and are often being used, in combination with other tests, as an indicator for a person’s intelligence. By practicing them you can improve your numerical reasoning ability which can be of great help in daily life activities like loan calculations, groceries or during job applications in assessments.

Tests of the numerical sequences type are always based on a standard form. A row of numbers is presented of which you have to find the missing number. This may be at the beginning or middle of the sequence, but is usually at the end. By cleverly using mathematical actions like subtraction, addition, division and multiplication you should be able to solve the sequence and find the missing number. The numbers presented in these sequences can be either integer sequences or rational sequences.

Integer Number Sequences

The first type of numbers presented in number sequences is integer number sequences, which are a form or real numbers. As the word already indicates, integer stands for incorruptible and thus series of integer numbers consist of whole numbers without fractions or decimals. When these numbers are positive integer numbers like 0, 1, 2, 3 etc they are called natural numbers, when they are negative integer numbers like -1, -2, -3 etc they are called non natural numbers. Both these types of numbers can be present in integer number sequences, resulting in a sequence like the following:

-1, 1, 3, 5, 7, …

Next to the division of natural and non natural numbers, a second division can be made using the term explicit and implicit descriptions. Explicit number sequences can easily be solved by giving the sequence a formula, like the sequence shown above. The formula for this sequence is “2n−1″ for the nth term, meaning that you can chose any integer number for the letter “n” in the formula and it will generate a number in the sequence, for instance: n=3 will generate 2*3-1 = 5 as shown in the example.

An implicit number sequence is given by a relationship between its terms. For example, the Fibonacci sequence as shown below:

0, 1, 1, 2, 3, 5, 8, 13, …

This number sequence is formed by starting with 0 and 1 and then adding any two previous terms to obtain the next one. This relationship is called an implicit description, since you cannot define this in such an easy formula with only one variable as in an explicit definition.

Rational Number Sequences

Unlike integers, rational numbers are numbers which can be written as a fraction or quotient where numerator and denominator both consist of integers, meaning that top and bottom of the fraction are whole numbers. Rational numbers can also be written by decimal expansion which either terminates after a finitely amount of numbers or repeats the same sequence over and over. Examples of rational numbers are ½, ¾, 1.75 and 3.25.

Next to rational numbers, also irrational numbers exists. These sequences consist of real numbers which cannot be expressed as a fraction, but only via expansion in decimals. Even then the decimals are not terminated after a finite amount of numbers but continue without repetition of the sequence. Examples of rational numbers are the square root of 2, pi and e.

As explained above number sequences exist in many forms and types. In order to improve your numerical reasoning skills it is best to practice all these different types and forms in order to master them and be of great help in everyday life.