Three Consecutive Numbers are the numbers that follow each other from the smallest number to the largest number. There are two types of consecutive numbers. They are even consecutive numbers and odd consecutive numbers. Know more on Consecutive Numbers Definition, Facts, Formulas, Procedure on How to find the Three Consecutive Numbers when Sum or Product is known. Have a look at the examples related to three consecutive numbers.

Also, Read: Prime and Composite Numbers

## Consecutive Numbers – Definition

Consecutive Numbers are the sequence or chain of numbers where each number is one more than the previous number. Consecutive Numbers are represented as n, n + 1, n + 2, n + 3, n + 4, …….

### Consecutive Numbers Formula

The formula to find the three consecutive numbers is n, n + 1, n + 2.

The formula for consecutive even numbers are 2n, 2n + 2, 2n + 4, 2n + 6,…

The formula for consecutive odd number are 2n + 1, 2n + 3, 2n + 5, 2n + 7,…

### How to find Three Consecutive Numbers?

Follow the simple steps provided to know about the procedure for finding the three consecutive numbers. They are as follows

- We know the three consecutive numbers are in general as n, n + 1, n + 2…
- You can find the value of integer ‘n’ you will be given either three consecutive numbers sum or product.
- Frame an equation on what the question is asked for.
- Solve for the variable ‘n’ as per the equation and then substitute the value of n in the consecutive numbers.

### Three Consecutive Numbers Examples with Solutions

**Example 1.**

What are the first three consecutive natural numbers?

**Solution:**

Natural Numbers are the numbers that start with 1.

N = 1, 2, 3, 4, 5, 6….

The formula for three consecutive numbers is n, n + 1, n + 2

1, 1 + 1, 1 + 2 = 1, 2, 3

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

**Example 2.**

Find the three consecutive numbers of 54.

**Solution:**

Let n be 54.

The formula to find the three consecutive numbers is n, n + 1, n + 2.

n = 54

n + 1 = 55

n + 2 = 56

n + 3 = 57

Thus the three consecutive numbers after 54 are 55, 56, 57.

**Example 3.**

What is the sum of three consecutive odd numbers?

**Solution:**

The formula for consecutive even numbers are 2n, 2n + 2, 2n + 4, 2n + 6,…

2n + 2n + 2 + 2n + 4

For n = 1

2n = 2(1) = 2

2n + 2 = 2(1) + 2 = 2 + 2 = 4

2n + 4 = 2(1) + 4 = 2 + 4 = 6

Thus the three consecutive even numbers are 2, 4, 6

**Example 4.**

The sum of three consecutive even numbers is 84. How do you find the numbers?

**Solution:**

Given,

The sum of three consecutive even numbers is 84.

The formula for consecutive even numbers are 2n, 2n + 2, 2n + 4.

2n + 2n + 2 + 2n + 4 = 84

6n + 6 = 84

6n = 84 – 6

6n = 78

n = 78/6

n = 13

**Example 5.**

The sum of three consecutive odd numbers is 27, how do you find the numbers?

**Solution:**

Given,

The sum of three consecutive odd numbers is 30

The formula for consecutive odd number are 2n + 1, 2n + 3, 2n + 5

2n + 1 + 2n + 3 + 2n + 5 = 27

6n + 9 = 27

6n = 18

n = 18/6

n = 3

2n + 1 = 2(3) + 1 = 6 + 1 = 7

2n + 3 = 2(3) + 3 = 6 + 3 = 9

2n + 5 = 2(3) + 5 = 6 + 5 = 11

Thus the three consecutive odd numbers are 7, 9, 11.

### FAQs on Three Consecutive Numbers

**1. What are Consecutive Numbers?**

The Numbers that follow each other from smallest to largest are known as Consecutive Numbers.

**2. The Sum of Three Consecutive Integers is 48. How do you find the Numbers?**

Three Consecutive Integers Sum is 48 i.e. n+n+1+n+2 = 48

3n+3=48

3n=48-3

3n=45

n=45/3 =15

Substituting the n value in the formula for three consecutive numbers we have n =15, n+1 = 15+1, n+2 =15+2

Thus, three consecutive integers are 15, 16, 17.

**3. What is the algebraic expression for the sum of three consecutive integers?
**

The Sum of Three Consecutive Integers is 3 times the middle value i.e. 3n

**4. What is the product of three consecutive integers?
**

The Product of Three Consecutive Integers is always divisible by 6.