Basic Concept of Series The class is “Chapter 4, Electrical Circuit” of the Basic Electricity course. This class is taught in Bangladesh Technical Education Board Polytechnic Discipline Diploma in Electrical, “1st Semester, Electrical Technology”.

## Basic Concept of Series

A series is an ordered collection of figures or numbers or words or alphabets. A sequence of numbers that follow a particular pattern is called a number series. In number series questions, some specific pre-decided rules are hidden and the candidate needs to find that hidden rule to arrive at the 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 the 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 the 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 the name suggests this series is a combination of arithmetic and geometric series. An important property of such a 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 are increasing or decreasing

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

Here the difference increases from left to right

- In the number series with an increasing or decreasing difference, the differences between the two consecutive numbers are decreasing

**Example:** 7, 16, 24, 31, 37, 42

Here the difference decreases 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 types of questions are a little complicated.

**Example:** 61, 72, 60, 73, 59, 74, 58, 75

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