# Consecutive Numbers

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## 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)  $$75, …, 77, 78, …, 80$$

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