What are Consecutive Numbers?
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. Let us learn more about consecutive numbers in this short 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’s 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 ordered 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.
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. For example, take the numbers 3, 5, 7, 9, and 11. These are called consecutive odd numbers because the difference between any predecessorsuccessor pair is 2. Take 5  3 = 2. Take 7  5 = 2. Hence, the difference between any predecessorsuccessor pair is 2.
Properties of Consecutive Numbers
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.
 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.
 Any n numbers in a row will have a multiple of n. For example, for 7 consecutive numbers in a row, there will be one multiple of 7.
 If n is an odd number, then the sum of n consecutive numbers will be divisible by n. For example, consecutive 3 numbers 5+6+7=18 and 18 is divisible by 3.
Consecutive Numbers Formula
For a number n, the next two consecutive numbers = (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(Aithmetic 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
 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, general form = 2n+1 (n=any integer)
 For an even consecutive number, general form = 2n (n=any integer)
Consecutive Numbers Solved 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. ∴ 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 implies that 3n + 6 = 24. Thus, 3n = 246 = 18. Now this implies that \implies 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. ∴ 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. ∴ The missing number is 20.
FAQs on Consecutive Numbers
What are 3 Consecutive Numbers?
Consecutive numbers are numbers that follow each other in order from the smallest number to the largest number. For example 1, 2, 3 are the first three consecutive natural numbers.
How do you Find Consecutive Numbers?
Write the given numbers in order from the smallest to the largest. Then find the difference between any predecessorsuccessor pair. The missing number in the consecutive number list is predecessor + difference
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.
Can Consecutive Numbers be Decimals?
Consecutive numbers cannot be decimal numbers 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.
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.
What is the Formula for Adding Consecutive Numbers?
The formula for adding consecutive numbers is n + (n+1) = 2n+1.
What is the Sum of Two Consecutive Numbers?
The sum of any two natural consecutive numbers is n + (n+1) = 2n+1
Can Consecutive Numbers be Fractions?
No, just like decimals, even fractions can't be counted as consecutive numbers.