# Quantitative Aptitude Concepts and Sample Questions Number Series and Sequences

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