# Number Series – Concept and Types

In this post we will understand the concept of number series which is important part of logical reasoning syllabus for competition exams like GMAT, CAT , SSC, IBPS, SBI, NDA and other notable exams.

we have tried to cover the basic details of number series along with the types of series which are frequently asked in the exams.

## Number Series

Number series is a form of series in which numbers or are arranged in particular order in different ways

Generally two types of questions are asked in number series

1. To find the missing number
2. To find an error in number

Types of number series –

### Prime number series

This type of series contain prime numbers in a consecutive way , alternate way or in a different way

Examples-

#### 7, 11, 13, 17, 19,?

This is a continues series of prime number
So our next number of the series should be 23

#### 3, 7, 13, 19, ?

This is an alternate series of prime numbers

Here we see that we get a gap of one prime number in between each element

#### 3, 7, 17, 31, ?

In this type of series we get a gap of one, two or more than two prime numbers

In above series we get a gap of one prime number in between first and second element
Then gap of two prime number between second and third element and so on.

### Difference series

In this type of series the difference of each consecutive elements is same
For example difference of first and second element is same as difference of second and third element and so on

Examples-

#### 2, 12,22, 32, ?

Here we take a difference of two consecutive elements

Here 42 is the right answer

#### 3, 20, 63, 144, 275, ?

Here we apply Difference of difference method

So our next element should be a difference of +12

### Multiplication series

In multiplication series the multiplication factor is same or may be different in  consecutive elements

Examples-

#### 6, 12, 36, 144, ?

Here we get a multiplication series of 2,3,4,5
So our next element should be 144×5=720

### Division series

-in division series the consecutive elements are in decreasing order with large difference. This series follow the same concept of multiplication series but in opposite way here the gap decreases rapidly

Examples-

#### 1000, 500, 250, 125, ?

Here second element is half of first element and third element is half of second element and so on

Here we get the last element as 125÷2=62.5

#### 15120, 2160, 360, 72, 18, ?

Here second element is seven times the first element
And third element is six times the first element and so on

### N2 series

In this type of series the consecutive elements are in square form either in ascending order or descending other

Examples-

#### 1, 4,9, 16, 25,?

Here all the elements are in square form so our last element should be 6=36

#### 196, 169, 144, ?

Here all elements are in squares of decreasing order
So our last element should be 112=121

### N2+1 series

when there is an addition of 1 in N2 series we get N2+1     series

Examples-

#### 10, 17, 26, 37, 50, ?

By taking difference of each consecutive element

This difference can be written as

So it is   N2+1 series and our last element should be  82+1=65

### 122, 145, 170,  ?

Our last element should be 142+1=197

### N2-1 series

when there is an subtraction of 1 in N2 series we get N2-1     series

Examples-

### 195, 168, 143, 120, ?

Here we get N2-1 series and our last element should be 102-1=99

#### 3, 8, 15, 24, ?

Here we get N2-1 series and our last element should be 62-1=35

### N²+N series

here we add same number to the square of that number

Examples

#### 20, 30, 42, 56, ?

Here we get N2+N series and our last element should be 82+8=72

### N²-N series

here we subtract same number to the square of that number

Example-

#### 56, 42, 30, 20, ?

Here we get N2-N series and our last element should be   42-4=12

### N³ series

here the elements are in cubic form ascending or descending  order

Example-

#### 8, 27, 64, 125, ?

Here we get N3 series and our last element should be   63=216

### N³+1 series

here we are at the same number to the cube of that   number

Example-

#### 126, 217, 344, ?

Here we get N3+1 series and our last element should be  83+1=513

### N³-1 series

here we subtract the same number to the cube of that number

Example-

#### 7, 26, 63, 124, ?

Here we get N3-1 series and our last element should be 63-1=215

### Alternating series–

It is a special type of series. Here we get a particular series in an alternate elements either addition subtraction multiplication or division

In this type of series our consecutive element are not continuously increases or decreases that is they are not arranged in a particular order

Example-

#### 18, 24, 21, 27, ?, 30

Here we get an alternate series of +3 so our fifth element should be 24

#### 15, 14, 19, 11, 23, ?

Here we get an alternate series of -3 and +4

So our last element should be 8

#### 50, 200, 100, 100, 200, 50, 400, ?

It is alternate multiplication and division series

Here we get an alternate series of ×2 and ÷2

So our last element should be 25

### Miscellaneous series

This is a mixture of all type of series

Examples-

#### 1, 2, 2, 4, 3, 8, 7, 10, ?

Here we get a alternate different type of addition series

#### 2, 7, 27, 107, ?

Here taking the difference of each consecutive element

Here arranging the difference we get following series

So our last element should be 107×4-1=427

### Some important points

• If there is a small gap of numbers between the consecutive elements then it may be difference series
• If there is a large gap of numbers between the consecutive elements then it may be division or multiplication series
• If there is not continuously increasing or decreasing order then it may be in alternate series
• If the elements of the series are near to the square or cube of any numbers then we do some addition or subtraction to get the required elements of the series.