# Consecutive Numbers

## Introduction

Understanding consecutive numbers can be simplified by understanding the concept of predecessors and successors.

The number that is written immediately before a number is called its **predecessor**.

The number that is written immediately after a number is called its **successor**.

## Consecutive Numbers

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. They usually have a difference of \(1\) between every two numbers.

Note: The difference between any predecessor-successor pair is fixed.

Let’s look at a few examples of consecutive numbers.

**Example 1:**

In the above example, the difference between any predecessor-successor pair is \(1.\)

**Example 2:**

In the above example, the difference between any predecessor-successor pair is \(2.\)

**Example 3:**

In the above example, the difference between any predecessor-successor pair is \(6.\)

## Solved Examples

### Example 1:

Find out the missing number in the series.

**\[3, 4, 5, 6, …, 8, 9, 10\]**

The difference between any predecessor-successor pair is \(1.\)

The predecessor of the missing number is \(6.\)

The successor of the missing number is \(8.\)

The missing number is **predecessor \(+\) difference** \(= 6 + 1 = 7\)

Alternatively,

The missing number is **successor \(-\) difference** \(= 8 - 1= 7\)

Thus, the missing number is \(7.\)

### Example 2:

Find out the missing number in the series.

**\[4, 8, 12, ..., 20, 24, 28, 32\]**

The difference between any predecessor-successor pair is \(4.\)

The predecessor of the missing number is \(12.\)

The successor of the missing number is \(20.\)

The missing number is **predecessor **\(+\)** difference** \(= 12 + 4= 16\)

Alternatively,

The missing number is **successor \(-\) difference** \(= 20 - 4= 16\)

Thus, the missing number is \(16.\)

## Practise Questions

Find out the missing numbers in the following series.

(a) \(10, 15, …, 25, 30\)

(b) \(2, 4, 6, 8, …\)

(c) \(75, …, 77, 78, …, 80\)