Overview: Number Series | Reasoning and Military Aptitude Test for AFCAT PDF Download

Introduction

A series is an ordered collection of figures or numbers or words or alphabets. A sequence of numbers which follow a particular pattern is called number series. In number series questions, some specific pre-decided rules are hidden and the candidate needs to find at that hidden rule to arrive at correct answer.

For example, consider 1, 4, 7, 10, 13….. Here the difference between the consecutive numbers is three. It is important to note that in number series each number except the first number is related to the prior number with some specific rule.

Types of Number Series

There are many types of number series. A few of them are explained below,

Arithmetic Series: In this type the series progresses with addition or subtraction of some specific numbers. Here the DIFFERENCE between any successive terms is not very large, increases in a specific manner and is constant throughout the series.
Example: 5, 10, 17, 26, 37, 50, 65

Geometric Series: In this type the series progresses with addition or subtraction of some specific numbers. Here the RATIO between any successive terms is large, increases in a specific manner and is constant throughout the series.
Example: 4, 12, 36, 108, 324, 972

Arithmetico-Geometric Series: As name suggests this series is the combination of arithmetic and geometric series. An important property of such series is that the DIFFERENCE of successive terms is in geometric series.
Example: 1, 8, 22, 50, 106, 218

Product series: In this type of series, each term is multiplied by a fixed number or specific number pattern to get the next successive number. This can be of following types,

• Multiplication of the previous number by a fixed number
  Example: 2, 4, 8, 16, 32, 64, 128
  
• Multiplication of the previous number by the next decreasing number
  Example: 30, 180, 900, 3600, 10800, 21600
  
• Multiplication of the previous number by the next increasing number

  Example: 21, 105, 630, 4410, 35280
  

Difference Series: Difference series can be further classified as

• The number series with a constant difference, where there is always a constant difference between the two consecutive numbers.
  Example: 3, 6, 9, 12, 15, 18, 21
  Here the difference is increasing from left to right
• In the number series with an increasing or decreasing difference the differences between the two consecutive numbers is decreasing
  Example: 7, 16, 24, 31, 37, 42
  Here the difference is decreasing from left to right

Division series: In this type of series, each term is divided by a fixed number or specific number pattern to get the next successive number.
Example: 128, 64, 32, 16, 8

Square or cube series: This type of numbers series progresses with squaring or cubing of the numbers.
Example: 4, 16, 36, 64, 100 (squaring)
Example: 1, 8, 64, 125, 216, 343 (Cubing)

Mixed series: In this type, more than one series pattern is involved. Generally these type of questions are a little complicated.
Example: 61, 72, 60, 73, 59, 74, 58, 75