Types of Number Series

To level up the exam and set a moderate to difficult examination, many different types of questions are included in the general aptitude section. One such question which is present in almost all types of competitive exams is the question on number series.

A number series is an arrangement of the numbers as per some rules and formulas and the repetition or the adding of a type of number depends on the logic behind each type of number series.

Before understanding the number series and its type, it is important to understand the concept of the number line

What is a number line?

A number is a sort of visual representation of numbers so as to understand the series of numbers easily and smartly.

Numbers, when represented on the number line, help in identifying the place of the numbers easily. The numbers are placed at an equal interval on a line that is indefinite. This placing of the numbers helps in the identification of the type of number series and also helps in determining the gap that is kept between two numbers. This gap represents the formula that helps in the identification of the type of number series.

A number of lines extend in both directions that are horizontally as well as vertically. As a person moves towards the right, the value of the number increases, and as the person moves towards the left of the number line, the value of the number decreases.

A number line is highly useful because it helps in writing and understanding the numbers easily on it, and this visual representation helps in performing the basic mathematical operations on them easily. One can easily operate on these numbers with the help of the visual representation of the number line.

A number line consists of  three parts :

Negative side

Zero 

Positive side 

The negative side of the number line is present to the left of the 0 on the number line, whereas the positive side of the number has positive numbers. This clearly means that the numbers on the right side are larger than the numbers present on the left side of the number line.

Number series

The number series is the arrangement of the numbers in a particular order according to a definite interval. The numbers are arranged in a particular pattern that uses a definite rule to make a particular series.

For example, we have 2,4,6,8. When seeing this particular sequence of numbers, we notice that there is a gap of 2 digits between each number present in this series. This is also a type of number series.

Similarly, for all the hidden number series questions, there is a hidden hint which tells about the pattern that is followed in that particular series.

Types of Number Series and some examples Number series

The number series in mathematics is of diverse types based on the logic used behind each pattern.

The various types of number series are :

1. Arithmetic series
2. Geometric series
3. Arithmetic Geometric Series
4. Product Series

5 Difference Series

6 Division Series

7 Mixed Series

8 Square cube series

Arithmetic Series: Arithmetic Series is a series in which the progression of the numbers happens by subtraction and addition. Here, the difference between the numbers in the series is not very large, but there is a gap seen between each number. The gap between numbers is constant throughout the series.

For example, 5, 11, 17,21 

This is an example of arithmetic series.

Geometric Series : 

In this type of series, the progression of the numbers happens by subtraction and addition, but the difference between the numbers is large as compared to the geometric series.

Here it is observed that the difference between each number is very large. This ratio is seen to be throughout the series. 

For example : 4, 22, 56, 108

Arithmetico- Geometric Series 

This type of number series is a mix of both arithmetic and geometric series.

But in this type of series, it is observed that the difference seen in this series is kike that of the Geometric Series.

Product Series :

In this type of number series, the successive numbers are obtained by multiplying the digit by a fixed number or fixed number pattern to get the next successive number in the series.

There are two types of possibilities in the product series : 

1. Multiplying the number by a fixed number in the series
2. Multiplying the number by a previous number in the series

Difference Series 

In the difference series, the difference set throughout the series is uniform and equal. A constant difference is found between the consecutive numbers in the series. The difference between the series is constant but can be increasing or decreasing.

Division Series

In the division series, each digit is divided by a fixed number or in a fixed pattern to get the number series.

Square or cube series 

In this type of number series, the square or cube of a particular number is done to get a constant pattern throughout the series.

Conclusion 

The number series in mathematics helps in finding the pattern that is followed within the series.

The number series help in the prediction of the next or the previous number in the series.