Consecutive Numbers: Meaning, Types, Formulas and Examples

Learn the meaning of consecutive numbers with simple examples. Understand consecutive integers, even and odd numbers, formulas, sums, and how to solve consecutive number problems.

Shivam Singh28 Sept, 2026

What Are Consecutive Numbers?

Consecutive numbers are numbers that follow one another in order without skipping any number. For ordinary consecutive integers, the difference between two consecutive numbers is 1.

For example:

1, 2, 3, 4, 5

Each number is 1 more than the number before it.

1 and 2 are consecutive.
5 and 6 are consecutive.
10, 11 and 12 are consecutive.
20, 21, 22 and 23 are consecutive.

Simple Definition

Consecutive numbers are numbers that come one after another in a sequence without a gap.

For example, 7, 8, 9, 10 are consecutive numbers because no number is skipped.

Consecutive Numbers Meaning in Maths

In elementary mathematics, consecutive numbers usually means numbers that come one after another in counting order.

For example:

12, 13, 14, 15

The difference between each pair is 1:

13 − 12 = 1
14 − 13 = 1
15 − 14 = 1

So, these numbers are consecutive.

On a number line, consecutive integers are next to each other.

What Does “Consecutive” Mean?

Consecutive means following one another in order without interruption or a gap.

For example:

3, 4, 5 → consecutive
15, 16, 17 → consecutive
25, 27, 28 → not consecutive because 26 is missing

Also, check: Successor and Predecessor in Maths: Meaning, Definition, and Examples

Difference Between Two Consecutive Numbers

The difference between two consecutive integers is always 1.

If the first number is n, the next consecutive number is:

n + 1

For example, if:

n = 20

then:

n + 1 = 21

Therefore, 20 and 21 are consecutive numbers.

Important Difference

Ordinary consecutive numbers differ by 1, while consecutive even numbers and consecutive odd numbers differ by 2.

Type	Example	Difference
Consecutive integers	8, 9, 10	1
Consecutive even numbers	8, 10, 12	2
Consecutive odd numbers	7, 9, 11	2

Two Consecutive Numbers

Two consecutive numbers are two numbers that come immediately one after another.

If the first number is n, the two consecutive numbers are:

n and n + 1

Examples

4 and 5
10 and 11
25 and 26
99 and 100

Example: Find Two Consecutive Numbers Whose Sum Is 101

Let the first number be n.

The next consecutive number is n + 1.

So:

n + (n + 1) = 101

2n + 1 = 101

2n = 100

n = 50

Therefore, the two numbers are:

50 and 51

Check:

50 + 51 = 101

Also, check: Integers: Types, Rules, Properties, and Examples

Three Consecutive Numbers

If the first number is n, three consecutive numbers can be written as:

n, n + 1, n + 2

Example

If n = 15, the three consecutive numbers are:

15, 16, 17

Their sum is:

15 + 16 + 17 = 48

Finding Three Consecutive Numbers

Suppose the sum of three consecutive numbers is 72.

Let the numbers be:

n, n + 1, n + 2

Then:

n + (n + 1) + (n + 2) = 72

3n + 3 = 72

3n = 69

n = 23

Therefore, the numbers are:

23, 24 and 25

Check:

23 + 24 + 25 = 72

Properties of Consecutive Numbers

Consecutive numbers have several useful properties.

1. The Difference Is 1

For ordinary consecutive integers:

n + 1 − n = 1

Example:

18 and 19

19 − 18 = 1

2. Two Consecutive Integers Have HCF 1

The HCF of any two consecutive integers is always 1.

For example:

HCF(29, 30) = 1

Why?

Any common divisor of two numbers also divides their difference. Since:

30 − 29 = 1

their only positive common divisor is 1.

3. The Sum of Two Consecutive Integers Is Odd

One of two consecutive integers is always even and the other is odd.

Therefore, their sum is always odd.

Example:

8 + 9 = 17

20 + 21 = 41

4. Consecutive Even Numbers Differ by 2

Examples:

2, 4, 6, 8

Each number is 2 more than the previous number.

5. Consecutive Odd Numbers Differ by 2

Examples:

1, 3, 5, 7

Each number is 2 more than the previous number.

6. The Sum of Consecutive Odd Numbers Is Divisible by the Number of Terms

For example:

3 + 5 + 7 = 15

There are 3 terms:

15 ÷ 3 = 5

More generally, the sum of any fixed number of consecutive odd numbers is divisible by the number of terms.

Consecutive Numbers from 1 to 100

The numbers from 1 to 100 form a sequence of consecutive natural numbers:

1, 2, 3, 4, 5, ..., 98, 99, 100

No number is skipped.

There are:

100 − 1 + 1 = 100 numbers

So, there are 100 consecutive natural numbers from 1 to 100.

Types of Consecutive Numbers

The most common types discussed in school mathematics are:

Consecutive natural numbers
Consecutive integers
Consecutive even numbers
Consecutive odd numbers

1. Consecutive Natural Numbers

Natural numbers are commonly used as counting numbers:

1, 2, 3, 4, 5, ...

Therefore, consecutive natural numbers are numbers that follow each other without a gap.

Example:

5, 6, 7, 8, 9

Another example:

21, 22, 23, 24

2. Consecutive Integers

Integers include:

negative numbers
zero
positive numbers

Examples of consecutive integers include:

-3, -2, -1, 0, 1, 2

and:

5, 6, 7, 8

If the first integer is n, consecutive integers can be written as:

n, n + 1, n + 2, n + 3, ...

Can Negative Numbers Be Consecutive?

Yes.

For example:

-5, -4, -3, -2, -1

are consecutive integers because each number is 1 greater than the previous number.

3. Consecutive Even Numbers

Even numbers are integers divisible by 2.

Examples:

2, 4, 6, 8, 10

When even numbers occur consecutively within the sequence of even numbers, the difference between them is 2.

Formula

If the first consecutive even number is 2n, then the next even numbers can be written as:

2n, 2n + 2, 2n + 4, 2n + 6, ...

Example

If n = 5:

2n = 10

So, four consecutive even numbers are:

10, 12, 14, 16

4. Consecutive Odd Numbers

Odd numbers are integers that are not divisible by 2.

Examples:

1, 3, 5, 7, 9

Consecutive odd numbers have a difference of 2.

Formula

If the first consecutive odd number is 2n + 1, then the next odd numbers are:

2n + 1, 2n + 3, 2n + 5, 2n + 7, ...

Example

If n = 4:

2n + 1 = 9

Four consecutive odd numbers are:

9, 11, 13, 15

Consecutive Numbers Formulas

Formulas make it easier to represent consecutive numbers in algebra.

Formula for Consecutive Integers

If the first integer is n, then:

n, n + 1, n + 2, n + 3, ...

For example, if n = 12:

12, 13, 14, 15

Formula for Two Consecutive Integers

Two consecutive integers can be represented as:

n and n + 1

Example:

If n = 30:

30 and 31

Formula for Three Consecutive Integers

Three consecutive integers can be represented as:

n, n + 1, n + 2

Example:

20, 21, 22

Formula for Consecutive Even Numbers

Consecutive even numbers can be written as:

2n, 2n + 2, 2n + 4, 2n + 6, ...

Example:

For n = 3:

6, 8, 10, 12

Formula for Consecutive Odd Numbers

Consecutive odd numbers can be written as:

2n + 1, 2n + 3, 2n + 5, 2n + 7, ...

Example:

For n = 3:

7, 9, 11, 13

Quick Formula Table

Type	Algebraic form
Two consecutive integers	n, n + 1
Three consecutive integers	n, n + 1, n + 2
Four consecutive integers	n, n + 1, n + 2, n + 3
Consecutive even numbers	2n, 2n + 2, 2n + 4, ...
Consecutive odd numbers	2n + 1, 2n + 3, 2n + 5, ...

Sum of Consecutive Numbers

The sum of consecutive numbers can be found using different formulas depending on the sequence.

Students can strengthen their maths concepts through interactive learning resources on CuriousJr.

General Sum Formula

If the first term, last term and number of terms are known:

Sum = n/2 × (First term + Last term)

where n is the number of terms.

Example

Find the sum of the integers from 50 to 60.

First term = 50
Last term = 60

Number of terms:

n = 60 − 50 + 1 = 11

Therefore:

Sum = 11/2 × (50 + 60)

= 11/2 × 110

= 605

So, the sum is:

605

Sum of the First n Natural Numbers

For:

1 + 2 + 3 + ... + n

the formula is:

Sum = n(n + 1)/2

Example

Find the sum of the first 15 natural numbers.

Sum = 15(15 + 1)/2

= 15 × 16/2

= 120

Sum of the First n Even Numbers

The first n even numbers are:

2, 4, 6, ..., 2n

Their sum is:

n(n + 1)

Example

Find the sum of the first 5 even numbers.

Numbers:

2 + 4 + 6 + 8 + 10

Using the formula:

5(5 + 1) = 30

So, the sum is:

Sum of the First n Odd Numbers

The first n odd numbers are:

1, 3, 5, ..., (2n − 1)

Their sum is:

n²

Example

Find the sum of the first 8 odd numbers.

Sum = 8²

= 64

Check:

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

Consecutive Numbers Examples

Example 1: Find Two Consecutive Numbers Whose Sum Is 101

Let the first number be n.

The second number is n + 1.

Therefore:

n + n + 1 = 101

2n + 1 = 101

2n = 100

n = 50

The numbers are:

50 and 51

Example 2: Find Three Consecutive Even Numbers Whose Sum Is 96

Let the numbers be:

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

Their sum is:

2n + 2n + 2 + 2n + 4 = 96

6n + 6 = 96

6n = 90

n = 15

Therefore:

2n = 30

The three numbers are:

30, 32 and 34

Check:

30 + 32 + 34 = 96

Example 3: Find Four Consecutive Odd Numbers Whose Sum Is 200

Let the numbers be:

2n + 1, 2n + 3, 2n + 5, 2n + 7

Their sum is:

8n + 16 = 200

Therefore:

8n = 184

n = 23

The numbers are:

47, 49, 51 and 53

Check:

47 + 49 + 51 + 53 = 200

Example 4: Find Three Consecutive Integers Whose Sum Is 72

Let the numbers be:

n, n + 1, n + 2

Then:

n + n + 1 + n + 2 = 72

3n + 3 = 72

3n = 69

n = 23

Therefore, the numbers are:

23, 24 and 25

Example 5: Find Five Consecutive Integers Starting From 18

Start with:

Add 1 each time:

18, 19, 20, 21, 22

These are five consecutive integers.

How to Identify Consecutive Numbers

Use these simple steps:

Step 1: Put the numbers in order

Example:

12, 13, 14, 15

Step 2: Find the difference between adjacent numbers

13 − 12 = 1

14 − 13 = 1

15 − 14 = 1

Step 3: Check whether the difference remains the same

If the difference is 1 throughout, the numbers are consecutive integers.

For even or odd sequences, a difference of 2 may indicate consecutive even or consecutive odd numbers.

Example

4, 5, 6, 7 → consecutive integers

4, 6, 8, 10 → consecutive even numbers

3, 5, 7, 9 → consecutive odd numbers

4, 6, 9, 10 → not a consecutive sequence of integers, even numbers, or odd numbers

Consecutive Numbers vs Consecutive Even and Odd Numbers

Feature	Consecutive Numbers/Integers	Consecutive Even Numbers	Consecutive Odd Numbers
Example	5, 6, 7	4, 6, 8	5, 7, 9
Difference	1	2	2
Can include zero?	Yes, for integers	Yes	No
Basic form	n, n + 1	2n, 2n + 2	2n + 1, 2n + 3

Common Mistakes

Mistake 1: Skipping a number

5, 6, 8 are not consecutive integers because 7 is missing.

Correct example:

5, 6, 7, 8

Mistake 2: Confusing even numbers with ordinary consecutive numbers

2, 4, 6 are consecutive even numbers, but they are not consecutive integers because the difference is 2.

Mistake 3: Using the wrong algebraic form

For consecutive integers:

n, n + 1, n + 2

For consecutive even numbers:

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

For consecutive odd numbers:

2n + 1, 2n + 3, 2n + 5

Mistake 4: Forgetting zero when working with integers

Zero is an integer.

So:

-2, -1, 0, 1, 2

is a sequence of consecutive integers.

Quick Revision

Consecutive numbers follow one another without a gap.
Consecutive integers have a difference of 1.
Two consecutive integers can be written as n and n + 1.
Three consecutive integers can be written as n, n + 1, n + 2.
Consecutive even numbers have a difference of 2.
Consecutive odd numbers have a difference of 2.
Consecutive integers can be positive, negative, or include zero.
The HCF of two consecutive integers is always 1.
The sum of two consecutive integers is always odd.
Sum of the first n natural numbers = n(n + 1)/2.
Sum of the first n even numbers = n(n + 1).
Sum of the first n odd numbers = n².

Consecutive Numbers FAQ

1. What are consecutive numbers in maths?

Consecutive numbers are numbers that come one after another in order without skipping any number. For example, 6, 7, 8 and 9 are consecutive integers.

2. Can consecutive numbers include zero?

Yes. When talking about consecutive integers, zero can be included. For example, -2, -1, 0, 1 and 2 are consecutive integers.

3. Why is the HCF of two consecutive numbers always 1?

For two consecutive integers, the difference is 1. Any common divisor must divide their difference, so it must divide 1. Therefore, their HCF is always 1.

4. Can negative numbers be consecutive?

Yes. Negative integers can be consecutive. For example, -5, -4, -3 and -2 are consecutive integers because each number is 1 greater than the previous one.

5. What is the formula for consecutive numbers?

For consecutive integers starting with n, the sequence is n, n + 1, n + 2, n + 3, .... For consecutive even numbers, use 2n, 2n + 2, 2n + 4, ..., and for consecutive odd numbers, use 2n + 1, 2n + 3, 2n + 5, ....