Consecutive Numbers – Meaning, Types, Formulas & Examples Explained

Consecutive Numbers

Consecutive numbers are numbers that come one after another in order without skipping any. So, when teachers ask, “What are Consecutive Numbers?”, students can say that each number in the series has a fixed difference from the next. 

To understand better, we also use the ideas of successors and predecessors. The number right before another number is its predecessor, and the number right after is its successor. For example, in the numbers 1, 2, 3, 4, and 5, the predecessor of 2 is 1, and its successor is 3. 

Consecutive numbers are numbers that follow each other in order, with a difference of 1 between each number. They come one after another without skipping any number. For example, 1, 2, 3, 4, 5 are consecutive numbers. These numbers are used in many mathematical problems and everyday situations like seating arrangements and counting sequences.

What is Consecutive Numbers?

Consecutive numbers are numbers that come right after each other in a continuous sequence. Each number is one more than the previous number. For example, if you start counting from 5, the next consecutive numbers are 6, 7, 8, and so on. These numbers follow a clear order without any gaps between them.

Consecutive Numbers Meaning in Maths

Meaning of Consecutive numbers is the numbers that come one after another in the correct counting order with a fixed difference between each successor. 

For natural numbers, this difference is always 1, which makes it easy to recognise them on the number line. For example, 5, 6, 7, 8, and 9 are consecutive numbers because each number is exactly one more than the one before it. 

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Properties of Consecutive Numbers

To understand consecutive numbers better, let’s look at their basic properties

• The HCF of two consecutive numbers is always 1.  For example, the HCF of 29 and 30 is 1.

• Consecutive numbers differ by 1, while consecutive even or odd numbers differ by 2. For example, 6 and 7 differ by 1, while 14 and 16 differ by 2.

• The sum of two consecutive numbers is always odd. When two consecutive even numbers are added, the result is even, and when two consecutive odd numbers are added, the result is also even. For example, 9 + 10 = 19 (odd) and 13 + 15 = 28 (even).

• The sum of consecutive odd numbers is always divisible by the number of terms in the sequence. For example, 1 + 3 + 5 = 9, and 9 ÷ 3 = 3.

Read More:  Counting Numbers

Definition of Consecutive Number

A consecutive number is defined as a number that is next in order to another without any gap or interruption. It follows the one before it immediately in a counting sequence. So, if you take any number, the consecutive number after it will be one more than that number.

Consecutive Numbers 1 to 100

Consecutive numbers from 1 to 100 are all the numbers starting at 1 and going straight to 100 in order without skipping any number. This means the series is 1, 2, 3, 4, all the way up to 100. These numbers help in learning to count and solving many math problems involving sequences.

Types of Consecutive Numbers

Consecutive numbers are grouped in four different ways. Let’s understand each types of consecutive numbers in detail below:

1. Consecutive Natural Numbers

Natural numbers  are the numbers used for counting, starting from 1 and going upward. Consecutive natural numbers are simply these numbers placed in order from smaller to larger without any gaps. Example: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

2. Consecutive Even Numbers

Even numbers are those divisible by 2, such as 2, 4, 6, 8. When they appear one after the other, with a difference of 2 between them, they are called consecutive even numbers. 

Example: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. Here every number can be divided by 2, and each one is exactly two more than the previous one.

3. Consecutive Odd Numbers

Odd numbers are those that cannot be divided evenly by 2, such as 1, 3, 5, 7. When they appear one after the other, with a difference of 2, they are called consecutive odd numbers.

Example: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19

This sequence is different from even numbers because none of the numbers can be divided by 2.

4. Consecutive Integers

Integers include all whole numbers, both positive and negative, along with zero. Consecutive integers are those that follow one another on the number line, always with a difference of 1.

They can be:

• Positive consecutive integers: 0, 1, 2, 3, 4, 5...

• Negative consecutive integers: -1, -2, -3, -4, -5...

Read More: Rounding Numbers

Consecutive Numbers Formulas

Consecutive numbers formulas make it easier to write, identify, and solve problems related to numbers that follow each other in order. Instead of adding or writing each number one by one, formulas give a quick way to represent them and find their sums. The main formulas for consecutive numbers are:

1. Consecutive Integers Formula

Integers are whole numbers that can be positive, negative, or zero. The difference between two consecutive integers is always 1.

Formula: If n is an integer, the next consecutive integer is n + 1.

Example: If n = 15, the next three consecutive integers are 15, 16, 17, 18.

2. Natural Consecutive Numbers Formula

Natural numbers are counting numbers (1, 2, 3, …). Consecutive natural numbers follow one another in order with no gaps.

Formula: a, a + 1, a + 2, a + 3 … (where a is the first natural number)

Example: If a = 7, then the consecutive natural numbers are 7, 8, 9, and 10.

3. Consecutive Even Numbers Formula

Even numbers are divisible by 2. Consecutive even numbers always have a difference of 2.

Formula: 2a, 2a + 2, 2a + 4, 2a + 6 … (where a is any integer)

Example: If a = 6, then 2a = 12. The consecutive even numbers are 12, 14, 16, 18.

4. Consecutive Odd Numbers Formula

Odd numbers are not divisible by 2. Consecutive odd numbers also have a difference of 2.

Formula: 2a + 1, 2a + 3, 2a + 5, 2a + 7 … (where a is any integer)

Example: If a = 3, then 2a + 1 = 7. The consecutive odd numbers are 7, 9, 11, 13.

Read More: Zero divided by a number

Sum of Consecutive Numbers

Let’s learn to calculate sum of consecutive numbers using consecutive numbers formulas discussed above:

1. General Formula for Consecutive Numbers

If the first term and last term are known, the sum of all consecutive numbers in between is:

Formula: Sum = n/2 × (First Term + Last Term)

where n = number of terms.

Example: Find the sum of integers from 50 to 60.

n = 60 – 50 + 1 = 11

Sum = 11 ÷ 2 × (50 + 60) = 11 ÷ 2 × 110 = 11 × 55 = 605

2. Sum of Consecutive Natural Numbers

For the first n natural numbers (1, 2, 3, …, n):

Formula: Sum = n(n+1)/2

Example: Find the sum of the first 15 natural numbers.

Sum = 15 × (15 + 1) ÷ 2 = 15 × 16 ÷ 2 = 120

3. Sum of Consecutive Even Numbers

For the first n even numbers:

Formula: Sum = n(n+1)

Example: Find the sum of the first 5 even numbers.

Numbers: 2, 4, 6, 8, 10

Sum = 5 × (5 + 1) = 5 × 6 = 30

4. Sum of Consecutive Odd Numbers

For the first n odd numbers:

Formula: Sum = n2

Example: Find the sum of the first 8 odd numbers.

Numbers: 1, 3, 5, 7, 9, 11, 13, 15

Sum = 8² = 64

Also read: Quick Calculation Techniques

Consecutive Numbers Examples

Here are some consecutive numbers  examples that show how these  numbers can be used in maths problems.

1. Find two consecutive integers whose sum is 101.

Solution:

Let the numbers be n and n + 1.

n + (n + 1) = 101

2n + 1 = 101

2n = 100

n = 50

So, the two consecutive integers are 50 and 51.

2. The sum of three consecutive even numbers is 96. Find the numbers.

Solution:

Let the even numbers be 2a, 2a + 2, 2a + 4.

Their sum = 2a + (2a + 2) + (2a + 4) = 6a + 6

Given 6a + 6 = 96

6a = 90

a = 15

So, the consecutive even numbers are 30, 32, and 34.

3. The sum of four consecutive odd numbers is 200. Find the numbers.

Solution:

Let the odd numbers be 2b + 1, 2b + 3, 2b + 5, 2b + 7.

Their sum = (2b + 1) + (2b + 3) + (2b + 5) + (2b + 7)

= 8b + 16

Given 8b + 16 = 200

8b = 184

b = 23

So, the consecutive odd numbers are 47, 49, 51, and 53.

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