Number Series

What is Number Series?

A series is an informally speaking of numbers. it is the sum of the terms of a sequence. Finite terms and series are defined by first and last terms while infinite series is endless. Number series is a form of series in which particular numbers are present in a particular order and missing numbers are to find out.

A series is solved by particular number series tricks, formulas, attitudes of a person. There are various types of series present in the exam. Series can be of many types of Numbers like Natural numbers, Whole numbers, Contagious numbers etc. A sequence is described as a list of elements with a particular order.

In competitive exams number series are given and where you need to find missing numbers. The number series are come in different types. At first you have to decided what type of series are given in papers then according with this you have to use shortcut tricks as fast as you can .

Different types of Number series?

There are multiple types of number series available –

1. Integer Number Sequences:– There are particular formulas tricks to solve number series. Each number series question is solved in a particular manner. This series is the sequence of real numbers decimals and fractions. Number series example of this is like 1.3.5.9….. etc. in which what should come next is Solved by number series shortcuts tricks performed by the candidate.
2. Rational Number Sequences:– These are the numbers which can be written as a fraction or quotient where numerator and denominator both consist of integers. An example of this series is ½, ¾, 1.75 and 3.25.
3. Arithmetic Sequences:– It is a mathematical sequence which consisting of a sequence in which the next term originates by adding a constant to its predecessor. It is solved by a particular formula given by the mathematics Xn = x1 + (n – 1)d. An example of this series is 3, 8, 13, 18, 23, 28, 33, 38, in which number 5 is added to its next number.
4. Geometric Sequences:– It is a sequence consisting of a multiplying so as to group in which the following term starts the predecessor with a constant. The formula for this series is Xn= x1 r n-1. An example of this type of number sequence could be the following:
   2, 4, 8, 16, 32, 64, 128, 256, in which multiples of 2 are there.
5. Square Numbers:– These are also known as perfect squares in which an integer is the product of that integer with itself. Formula= Xn= n2. An example of this type of number sequence could be the following:
   1, 4, 9, 16, 25, 36, 49, 64, 81, ..
6. Cube Numbers:– Same as square numbers but in these types of series an integer is the product of that integer by multiplying 3 times. Formula= Xn=N3. Example:-1, 8, 27, 64, 125, 216, 343, 512, 729, …
7. Fibonacci Series:– A sequence consisting of a sequence in which the next term originates by addition of the previous two
   Formula = F0 = 0 , F1 = 1
   Fn = Fn-1 + Fn-2. An example of this type of number sequence could be the following:
   0, 1, 1, 2, 3, 5, 8, 13, 21, 34,...

Numerical Series Examples

1.) Examine the difference between adjacent numbers.

→ In a simple series, the difference between two consecutive numbers is constant.

Example: 27, 24, 21, 18, __

Rule: There is a difference of (-3) between each item. The missing number in this case is 15.

→ In a more complex series, the differences between numbers may be dynamic rather than fixed, but there is still a clear logical rule.

Example: 3, 4, 6, 9, 13, 18, __

Rule: Add 1 to the difference between two adjacent items. After the first number add 1, after the second number add 2, and after the third number add 3, etc. In this case, the missing number is 24.

2.) See whether there is a multiplication or division pattern between two adjacent numbers.

Example: 64, 32, 16, 8, __

Rule: Divide each number by 2 to get the next number in the series. The missing number is 4.

3.) Check whether adjacent numbers in the series change based on a logical pattern.

Example: 2, 4, 12, 48, __

Rule: Multiply the first number by 2, the second number by 3 and the third number by 4, etc. The missing item is 240.

4.) See if you can find a rule that involves using two or more basic arithmetic functions (+, -, ÷, x). In the series below, the functions alternate in an orderly fashion.

Example: 5, 7, 14, 16, 32, 34, __

Rule: Add 2, multiply by 2, add 2, multiply by 2, etc. The missing item is 68. Tip: Series in this category are easy to identify. Just look for numbers that do not appear to have a set pattern.

Important:

In a series that involves two or more basic arithmetic functions, the differences between adjacent items effectively create their own series. We recommend that you try to identify each pattern separately.

Example: 4, 6, 2, 8, 3, __

Rule: In this series, the differences themselves create a series: +2, ÷3, x4, -5. The numbers advance by intervals of 1, and the arithmetic functions change in an orderly sequence. The next arithmetic function in the series should be +6, and so the next item in the series is 9 (3+6 = 9).