Consecutive Numbers
Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written in a series where the difference between the numbers is fixed and where no numbers are skipped in between. Let us learn more about consecutive numbers in this article.
1.  What are Consecutive Numbers? 
2.  Consecutive Even Numbers 
3.  Consecutive Odd Numbers 
4.  Properties of Consecutive Numbers 
5.  Consecutive Numbers Formula 
6.  FAQs on Consecutive Numbers 
What are Consecutive Numbers?
To understand consecutive numbers, we 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, and 5. The predecessor of 2 is 1, and 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 that the difference between any predecessorsuccessor pair is fixed. Let us look at a few examples of consecutive numbers.
In the above example, the difference between any predecessorsuccessor pair is 1. If we denote the 1st number as n, then the consecutive numbers in the series will be n, n+1, n+2, n+3, n+4, and so on.
Consecutive Even Numbers
We know that even numbers are those numbers that 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 arranged as 2, 4, 6, 8, 10, 12 when written from the smallest to the largest. We can see that the difference between any predecessorsuccessor pair is 2. Therefore, these numbers form the list of consecutive even numbers.
Consecutive Odd Numbers
We know that odd numbers are those numbers which cannot be completely divided by 2. When we arrange them in ascending order, we can see that the difference between them is always 2. For example, the numbers 3, 5, 7, 9, and 11 are called consecutive odd numbers because the difference between any predecessorsuccessor pair is 2, like, 5  3 = 2 and 7  5 = 2.
Properties of Consecutive Numbers
Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The following points show the properties of consecutive numbers.
 In consecutive numbers, the difference between any predecessorsuccessor pair is fixed. If we denote the 1st number as n, then the consecutive numbers in the series will be n, n+1, n+2, n+3, n+4, and so on.
 For any two consecutive odd numbers, the difference is 2. For example, 3 and 5 are two consecutive odd numbers, their difference = 5  3 = 2.
 For any two consecutive even numbers, the difference is 2. For example, 6 and 8 are two consecutive even numbers, their difference = 8  6 = 2.
 If 'n' is an odd number, then the sum of 'n' consecutive numbers will be divisible by 'n'. For example, the sum of these 3 consecutive numbers is 5+6+7=18 and 18 is divisible by 3.
Consecutive Numbers Formula
For a number n, the next two consecutive numbers are (n + 1) and (n + 2). Given below are more consecutive number formulas.
 The formula for adding 'n' consecutive numbers = [a + (a + 1) + (a + 2) + .... {a + (n1)}]. So, the sum of 'n' consecutive numbers or sum of 'n' terms of AP (Arithmetic Progression) = (n/2) × (first number + last number).
 Even Consecutive Numbers Formula = 2n, 2n+2, 2n+4, 2n+6,…
 Odd Consecutive Numbers Formula = 2n+1, 2n+3, 2n+5, 2n+7,…
Important Points
Here is a list of some important points that should be remembered while working with consecutive numbers.
 To find the missing numbers in a series, write the numbers in ascending order and find the difference between any predecessorsuccessor pair.
 If we denote the 1^{st} number as n, then the consecutive numbers in the series will be n+1, n+2, n+3, n+4, and so on.
 If we denote the 1^{st} integer as n, the consecutive even or consecutive odd integers will be n+2, n+4, n+6, n+8, and so on.
 For an odd consecutive number, the general formula = 2n+1 (where 'n' = any integer)
 For an even consecutive number, the general formula = 2n (where 'n' = any integer)
Topics Related to Consecutive Numbers
Consecutive Numbers Examples

Example 1: Find the missing number in the series: 4, 8, 12, ..., 20, 24, 28, 32.
Solution:
The difference between any predecessorsuccessor 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 2: 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. This leads to 3n + 6 = 24, and n = 6. Therefore, the numbers are n = 6, n + 2 = 6 + 2 = 8 , and n + 4 = 6 + 4 = 10 . Now, let us add the three numbers and verify our solution. Thus, 10 + 8 + 6 = 24. Therefore, the numbers are 6, 8, and 10.

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 predecessorsuccessor 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.
Practice Questions on Consecutive Numbers
FAQs on Consecutive Numbers
What are Consecutive Numbers in Math?
Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. The difference between consecutive numbers is always fixed and it follows a pattern. For example 1, 2, 3 are the first three consecutive natural numbers.
What are Consecutive Positive Numbers?
Consecutive positive numbers are the set of positive numbers whose difference is 1. For example, 1, 2, 3, 4, 5, 6 ... is the set of consecutive positive numbers.
Can Consecutive Numbers be Decimals?
No, consecutive numbers cannot be decimal numbers because there are several numbers between every two decimal numbers. For example, in the list of these numbers: 3.1, 3.2 and 3.3..., many decimal numbers like 3.11, 3.111, 3.1111... exist between them.
When are 2 Numbers Considered Consecutive Numbers?
Two numbers that follow each other in order are called two consecutive numbers. For example:
 1 and 2 are two consecutive natural numbers.
 3 and 6 are two consecutive multiples of 3.
 10, 20 are two consecutive multiples of 10.
What are Odd Consecutive Numbers?
We know that odd numbers are those numbers which are not completely divisible by 2. When we arrange odd numbers in ascending order, we can see that the difference between them is always 2. Therefore, when odd numbers are arranged as 3, 5, 7, 9, and 11, they are called consecutive odd numbers because these numbers have a fixed difference of 2 between any predecessorsuccessor pair.
What are Non Consecutive Numbers?
Non consecutive numbers are those numbers that form a list in which there is no pattern or any fixed difference between a predecessor and a successor. For example, 2, 5, 17, 21 and so on are non consecutive numbers.
Can Consecutive Numbers be Fractions?
No, just like decimals, fractions cannot be considered as consecutive numbers because there are several fractions existing in between two fractions.
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