Series Test

A series is a continuous repetition of an occurrence that has a specific periodic interval between two elements.

A number series is defined as a sequential order of numbers that differ and repeat with a specific periodic interval. In mathematical language, a number series is a sequence of numbers that are represented in a specific order.

Example- 2, 4, 6, 8, 10, 12, etc.

Types of Number Series

Rational Number Series

A number series that can be noted down in the form of fractions or decimals or a number that consists of a numerator and a denominator is called a rational number series.

Example- 1/4, 1/2, 1, 3/2, etc.

Integer Number Series

A number series which consists of repetition in a specific order of integers, real numbers or fractions is called an integer number series.

Example-  1, 7, 14, 21, 28, 35, 42, etc.

Arithmetic Number Series (Arithmetic progression)

An Arithmetic Progression (AP) is a sequence where each term is found by adding a fixed number/difference to the previous term. This known difference is called a common difference.

Example- 2, 4, 6, 8, 10, 12, …..n

There is a difference of 2 between each term of the above sequence.

Geometric Number Series (Geometric progression)

Geometric progression is a number series where to get the next term in the geometric progression, we will have to multiply each element of the sequence with a fixed term known as the common ratio, every time.

Example- 2, 4, 8, 16, 32, 64, 128,…..n

The following terms can be found by multiplying 2 to each term.

Harmonic Number Series (Harmonic progression)

A number series is said to be a harmonic progression if the reciprocal of the given terms are said to be in Arithmetic Progression (AP). In simple terms, if p, q, r, s, t, u are in AP then 1/p, 1/q, 1/r, 1/s, 1/t, 1/u are in HP.

Recursive Number Series

A number series in which the next term is formed by performing a certain task/operation on the previous term is called a recursive number series.

For example- xn-1, x, xn+1.

Certain operations are performed on each term to get a new term.

Square Number Series

This type of number series is a series of numbers which are perfect squares of a number. A number in this series is the result of the product of that number with itself. This type of Number Series can be formed by using the formula n2.

Example- 1, 4, 9, 16, 25, 36, 49, 64, 81, ……

Cube Number Series

This type of number series is a series of numbers which are perfect cubes of a number. A number in this series is the result of the product of that number three times with itself. This type of Number Series can be formed by using the formula n3.

Example- 1, 8, 27, 64, 125, 216, etc.

Fibonacci Number Series

A number series which is formed when an element of a number series is formed by the addition of the previous two elements of the series is called the Fibonacci Number Series.

Example- 0, 1, 1, 2, 3, 5, 8, 13, ….

The third term is formed by the addition of the first and second term that is 

0 + 1 = 1

The fourth term is formed by the addition of the second and third term that is 

1 + 1 = 2

The fifth term is formed by the addition of the third and fourth term that is 

1 + 2 = 3

The sixth term is formed by the addition of the fourth and fifth term that is 

2 + 3 = 5

Conclusion

Number series is considered to be a basic concept in the field of Mathematics and helps one to solve number series equations easily. These types of questions are used to test a student in various competitive examinations. 

One must know all the rules when it comes to a number series. Also, this topic is very vast and interesting if studied with focus and determination.