Number Series: Basic Concept, Types of Number Series, Tips and Tricks to Find out Pattern of number Sequence
Posted on : 19-12-2018 Posted by : Admin

Practice test on this topic

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

• In the number series with an increasing or decreasing difference the differences between the two consecutive numbers is increasing or decreasing

Example: 1, 2, 4, 7, 11, 16, 22

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

Practice test on this topic

Tricks to solve Number series Question

Number series questions are common in any competitive exam. Candidates can score good marks with just the basic knowledge of math. These questions are relatively easy provided the candidate is able to find out the hidden rule. Here Studyandscore provides you with basic tips and tricks to solve number series questions. After you read through this article, click below to revise and practice with our tests.

Let us see the types of number series questions and tricks to solve them

Practice test on this topic

Practice test on this topic 

Practice test on this topic

 

Techniques to know hidden number pattern

BASED ON DIFFERENCE BETWEEN TWO CONSECUTIVE TERMS OF A SERIES

Difference between two consecutive terms is same For example: $$\begin{gathered} 2\underset{+5}{\to }7\underset{+5}{\to }12\underset{+5}{\to }17 \\ 35\underset{-8}{\to }27\underset{-8}{\to }19\underset{-8}{\to }11 \end{gathered}$$

Difference between two consecutive terms is in arithmetic progression (AP) For example: $$\begin{gathered} 15\underset{+11}{\to }26\underset{+16}{\to }42\underset{+21}{\to }63 \\ 34\underset{-9}{\to }25\underset{-7}{\to }18\underset{-5}{\to }13 \end{gathered}$$ *Here 11, 16, 21 are in AP in example 1 whereas -9, -7, -5 are in AP example 2.

Difference between two consecutive terms is a perfect square For example: $$\begin{gathered} 7\underset{+3^2}{\to }16\underset{+5^2}{\to }41\underset{+7^2}{\to }90 \\ 70\underset{-4^2}{\to }54\underset{-3^2}{\to }45\underset{-2^2}{\to }41 \end{gathered}$$

Difference between two consecutive terms are multiples of a number For example: $$\begin{gathered} 11\underset{+12}{\to }23\underset{+24}{\to }47\underset{+48}{\to }95 \\ 204\underset{-44}{\to }106\underset{-33}{\to }127\underset{-22}{\to }105 \end{gathered}$$ *Here 12, 24, 48 are multiples of 12 in example 1 whereas -44, -33, -22 are multiples of 11 example 2.

Difference between two consecutive terms is a perfect Cube For example: $$\begin{gathered} 7\underset{+2^3}{\to }15\underset{+3^3}{\to }42\underset{+4^3}{\to }106 \\ 121\underset{-4^3}{\to }57\underset{-3^3}{\to }30\underset{-2^3}{\to }22 \end{gathered}$$

Difference between two consecutive terms is in geometric progression (GP) For example: $$\begin{gathered} 1\underset{+1}{\to }2\underset{+3}{\to }5\underset{+9}{\to }14\underset{+27}{\to }41 \\ 33\underset{-16}{\to }17\underset{-8}{\to }9\underset{-4}{\to }5\underset{-2}{\to }3 \end{gathered}$$ *Here 1, 3, 9, 27 are in GP in example 1 whereas -16, -8, -4, -2 are in GP example 2.

Practice test on this topic

BASED ON RATION BETWEEN TWO CONSECUTIVE TERMS OF A SERIES

Ratio between two consecutive terms is same For example: $$\begin{gathered} 3\underset{\times 5}{\to }15\underset{\times 5}{\to }75\underset{\times 5}{\to }375 \\ 32\underset{÷2}{\to }16\underset{÷2}{\to }8\underset{÷2}{\to }4 \end{gathered}$$

Ratio between two consecutive terms is a Prime number For example: $$\begin{gathered} 5\underset{\times 1}{\to }15\underset{\times 2}{\to }30\underset{\times 3}{\to }90\underset{\times 5}{\to }450 \\ 770\underset{÷11}{\to }70\underset{÷7}{\to }10\underset{÷5}{\to }2 \end{gathered}$$ *Here 2, 3, 5 are prime numbers in example 1 whereas 11, 7, 5 are prime numbers example 2.

Ratio between two consecutive terms is in arithmetic progression (AP) For example: $$\begin{gathered} 2\underset{\times 2}{\to }4\underset{\times 4}{\to }16\underset{\times 6}{\to }96 \\ 420\underset{÷5}{\to }84\underset{÷4}{\to }21\underset{÷3}{\to }7 \end{gathered}$$ *Here 2, 4, 6 are in AP in example 1 whereas 5, 4, 3 are in AP example 2.

Ratio between two consecutive terms is a perfect square For example: $$\begin{gathered} 3\underset{\times 2^2}{\to }12\underset{\times 4^2}{\to }192\underset{\times 6^2}{\to }6912 \\ 44100\underset{÷7^2}{\to }900\underset{÷5^2}{\to }36\underset{÷3^2}{\to }4 \end{gathered}$$

Ratio between two consecutive terms are multiples of a number For example: $$\begin{gathered} 5\underset{\times 2}{\to }10\underset{\times 4}{\to }40\underset{\times 8}{\to }320 \\ 972\underset{÷9}{\to }108\underset{÷6}{\to }18\underset{÷3}{\to }6 \end{gathered}$$ *Here 2, 4, 8 are multiples of 2 in example 1 whereas 9, 6, 3 are multiples of 3 example 2.

Ratio between two consecutive terms is a perfect Cube For example: $$\begin{gathered} 2\underset{\times 1^3}{\to }2\underset{\times 3^3}{\to }54\underset{\times 5^3}{\to }6750 \\ 13824\underset{÷4^3}{\to }216\underset{÷3^3}{\to }8\underset{÷2^3}{\to }1 \end{gathered}$$

Ratio between two consecutive terms is in geometric progression (GP) For example: $$\begin{gathered} 1\underset{\times 1}{\to }1\underset{\times 2}{\to }2\underset{\times 4}{\to }8\underset{\times 8}{\to }64 \\ 729\underset{÷27}{\to }27\underset{÷9}{\to }3\underset{÷3}{\to }1 \end{gathered}$$ *Here 1, 3, 9, 27 are in GP in example 1 where a -16, -8, -4, -2 are in GP example 2.

Practice test on this topic

---

---

Hope you have liked this post.

Please share it with your friends through below links.

All the very best from Team Studyandscore

“Study well, Score more…”