# What are Consecutive Numbers?

What are Consecutive Numbers?
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Explore the world of consecutive numbers by going through its various aspects and properties. Find answers to questions like what are consecutive odd and even numbers, how they are formed, and discover interesting facts around them.

In school, we always walk in a line. Don't we?

We stand one behind the other based on our height, or our teacher makes us stand in alphabetical order when we want to play some games.

What do you see here?

 We are in a line, following a pattern!

Numbers also follow each other, following a pattern.

Such a sequence of numbers is called consecutive numbers.

 1 What are Consecutive Numbers? 2 Learn These Along with Consecutive Numbers! 3 Examples on Consecutive Numbers 4 Interactive Questions on Consecutive Numbers

## What are Consecutive Numbers?

To understand consecutive numbers, we will first need to understand 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.

For example

consider the list of natural numbers 1,2,3,4,5...

• The predecessor of  2 is 1
• The successor of 2 is 3

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

If we denote the 1st number as $$n$$, then the consicutive numbers in the series  will be $$n+1$$, $$n+2$$, $$n+3$$, $$n+4$$, and so on.

Here is another example for you.

The difference between any predecessor-successor pair in this example is always 6, as they are all multiples of 6

Do you think there will be an odd number in the list of consecutive multiples of 6?

## Learn These Along with Consecutive Numbers!

Here are a few more lessons related to consecutive numbers.

These topics will not only help you master the concept for consecutive numbers, but also other topics related to it.

 Click on any of the short lessons you want to explore! PEMDAS Ordinal Numbers Composite Numbers Co-prime numbers Perfect Numbers Natural Numbers Prime Number

### Consecutive Even Numbers

We know that even numbers  are those numbers which end in 0, 2, 4, 6, and 8

Now let us consider the set of even numbers from 2 to 12 and write them in ascending order.

The numbers are ordered as 2, 4, 6, 8, 10, 12 when written from the smallest to the largest.

We can see that the difference between any predecessor-successor pair is 2

Can you identify the consecutive even numbers between 20 and 30?

### Consecutive Odd Numbers

We know that odd numbers are one less or one more than the even numbers.

When we arrange them in ascending order, we can see that the difference between them is always 2

In the above example, the difference between any predecessor-successor pair is 2

$$5-3 = 2$$

$$7-5 = 2$$ and so on.

## Solved Examples

 Example 1

Find the missing number in the series.

$3, 4, 5, 6, …, 8, 9, 10$

Solution:

The difference between any predecessor-successor pair in this series 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 $$= 8 - 1= 7$$

 $$\therefore$$ The missing number in the series is  7
 Example 2

Find the missing number in the series.

$4, 8, 12, ..., 20, 24, 28, 32$

Solution:

The difference between any predecessor-successor pair in this series 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 $$= 20 - 4= 16$$

 $$\therefore$$  The missing number in the series is 16
 Example 3

What is the third number in the given series if they are all consecutive multiples of an odd integer?

$5, 15, ___ , 25, 30$

Solution:

The difference between any predecessor-successor pair in this series is 5

The predecessor of the missing number is 15

The successor of the missing number is 25

The missing number is predecessor$$+$$ difference $$= 15 + 5= 20$$

 $$\therefore$$  The missing number is 20
 Example 4

Find the missing numbers in the following series.

$75, …, 77, 78, …, 80$

Solution:

The difference between any predecessor-successor pair in this series is 1

The predecessor of the first missing number is 75

The successor of the first missing number is 77

The missing number is predecessor$$+$$ difference $$= 75 + 1= 76$$

We see that numbers are in order: $$75, 76, 77, 78$$ and the difference is $$1$$

Thus, the next number in the series will be $$79$$

 $$\therefore$$ Missing numbers in the series are 76 and 79
 Example 5

The sum of three consecutive even numbers is 24.

What are the three numbers?

Solution:

Consecutive even numbers have a difference of 2 between them.

If the first number is $$n$$, then the second number is $$n+2$$ and the third number is $$n+4$$.

Given that their sum is  24, hence, we have:

$$n + n+2 + n+4 = 24$$

$$\implies 3n + 6 = 24$$

$$3n = 24-6 = 18$$

$$\implies n = 6$$

Therefore, the numbers are

$$n =6$$

$$n+2 = 6+2 = 8$$

$$n+4 = 6+4 = 10$$

Let us add the three numbers and verify our solution.

$$10+8+6 = 24$$

 $$\therefore$$  The numbers are 6, 8, and 10

Think Tank
1. Will the sum of two consecutive numbers be odd or even?
2. Find the difference between consecutive square numbers. Do you see a pattern? What is their difference?
3. Why is the product of 3 consecutive natural numbers always divisible by 6?

## Interactive Questions

Here are a few activities for you to practice.

Important Notes
1. To find the missing numbers in a series, write the numbers in ascending order and find the difference between any predecessor-successor pair.
2. If we denote the 1st number as $$n$$, then the consecutive numbers in the series will be $$n+1$$, $$n+2$$, $$n+3$$, $$n+4$$, and so on.
3. If we denote the 1st integer as $$n$$, the consecutive even or consecutive odd integers will be $$n +2$$, $$n +4$$, $$n +6$$, $$n +8$$, and so on.

## Summary

The magic of math lies in the amazing concepts that it is built upon. At Cuemath, we explore and interact with these concepts in a fun way!

The math journey around consecutive numbers starts with the basics of numbers and goes on to creatively crafting a fresh concept in the young minds. Done with real-life and relatable examples.

The best part, this isn’t the end. With a universe built around consecutive numbers at Cuemath, one can take their math journey forward with solved examples, practice questions, quizzes, worksheets, practice papers, and so much more. Again, all of it, exclusively around consecutive numbers.

## 1. What are 3 consecutive numbers?

Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number.

Example 1, 2, 3 are the first three consecutive natural numbers.

## 2. How do you find consecutive numbers?

1. Write the given numbers in order from the smallest to the largest.
2. Find the difference between any predecessor-successor pair
3. The missing number in the consecutive number list is predecessor $$+$$ difference

## 3. What are consecutive positive numbers?

Consecutive positive numbers are the set of positive numbers whose difference is 1.

$$1, 2, 3, 4, 5, 6...$$ is the set of consecutive positive numbers.

## 4. Can consecutive numbers be decimals?

Consecutive numbers cannot be a decimal number because there exist several decimal numbers between every decimal number.

For example, if we say $$3.1, 3.2, 3.3...$$ are consecutive numbers,  several decimal numbers like $$3.11, 3.111, 3.1111 ....$$ exist in between them.

## 5. What are 2 consecutive numbers?

Two numbers that follow each other in order are called 2 consecutive numbers.

Example: $$1,2$$ are 2 consecutive natural numbers.

$$3,6$$ are 2 consecutive multiples of 3.

$$10,20$$ are 2 consecutive multiples of 10.

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