Jagranjosh.com has brought some important concepts with sample questions to help you in you preparation and hard work for competitive exams.

**Number Series and Sequences** is an important topic for any competitive exam. Types of questions in this topic includes

- Find the missing term or next term in given series
- Find the wrong term in given series

**Number Series**

A number series is a sequence of many numbers written from left to right in a certain pattern. They always follow some pattern or the specific rules; we just have to recognize the pattern or rule to solve the questions.

**Prime Number Series**

In these types of series, a series is made by using prime numbers and arranging them in different patterns.

**Example 1. Find out the next term in the series? **

**7, 11, 13, 17, 19,………………..**

**Solutions**: Given series is a consecutive prime number series. Therefore, next term in series will be 23.

**Multiple Series**

In these types, series proceeds as a multiple of a specific numbers.

**Example: Find out the missing term in the series 4, 8, 16, 32, 64, ……………256.**

**Solutions:** Here, every next number is double the previous number.

Required number= 64 x 2 = 128

**Division Series**

As similar to Multiple series, the numbers in series are divided by some specific number.

**Example: Find out the missing term in the series, 80, 200, 500, ?, 3125**

**Solutions:** 80 x 5/2 = 200

200x 5/2 = 500

500 x 5/2 = 1250

1250 x 5/2 = 3125

Hence, missing term is 1250

**Difference or Addition Series **

In these types, the pattern followed is of adding or subtracting a specific number.

**Example:** Find out the missing term in the series 108, 99, 90, 81, ………………….63.

**Solutions:** Here, every next number is 9 less than the previous number.

Therefore, Required number = 81-9 = 72

**n ^{2 }Series **

The pattern followed in of adding or subtracting a specific number.

**Example:** find out the missing term in the series 4, 16, 36, 64,……………………….. 144.

Solution: This is a series of square of consecutive even numbers.

i.e 2^{2 }=4

4^{2} = 16

6^{2} = 36

8^{2} = 64

**10 ^{2}= 100**

12^{2} = 144

Hence missing term is 100

**(n ^{2}+1) Series**

Here 1 is added to the square term to form the series.

**Example: 10, 17, 26, 37, ……………………………65.**

**Solution: **Series Pattern is

3^{2 }+1=10

4^{2}+1 = 17

5^{2}+1=26

6^{2}+1= 37

**7 ^{2}+1= 50**

8^{2}+1= 65

Therefore, required number =50

**(n ^{2}-1) Series**

In this series 1 is subtracted from the square number like 1 was added (n2+1) series.

**Example**: find out the missing term in the series 0, 3, 8, 15, 24, ?, 48

Solution: Series Pattern is

12-1 = 0

22-1 = 3

32-1= 8

42-1=15

52-1=24

**62-1=35**

72-1= 48

Required number= 35

**(n ^{2}+n) Series**

In this series the same number is added to its square term to form series

Example: find out the missing term in the series 420,930, 1640, ………..3660.

Solution: Series pattern is 20^{2}+20, 30^{2}+30, 40^{2}+40, **50 ^{2}+50**

Required number = 50^{2}+50

Similar pattern will be applicable for n^{3} series