Consecutive Numbers

Consecutive numbers are those numbers that follow each other in a regular counting order or pattern. 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 the meaning of consecutive numbers, consecutive even numbers, consecutive odd numbers, the consecutive numbers formula along with some consecutive numbers examples in this article.

Consecutive numbers follow each other continuously in order. Let us first understand the concept of predecessors and successors to understand consecutive numbers. 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 Meaning

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 predecessor-successor pair is fixed. Let us look at a few examples of consecutive numbers.

In the above example, the difference between any predecessor-successor 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.

We know that even numbers are those numbers that are divisible by 2 and that end in 0, 2, 4, 6, or 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 predecessor-successor pair is 2. Therefore, these numbers form the list of consecutive even numbers.

We know that odd numbers are those numbers that are not divisible 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 predecessor-successor pair is 2, like, 5 - 3 = 2 and 7 - 5 = 2.

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 predecessor-successor 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.

The consecutive numbers formula is used to list consecutive numbers. 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 + (n-1)}]. 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,…

Consecutive Composite Numbers

We know that composite numbers are those numbers that have more than two factors. So, consecutive composite numbers are composite numbers listed in order. For example, if we want to write consecutive composite numbers from the set of natural numbers, it will be, 8, 9, 10. After this set, it can be 14, 15, 16, and so on. All these are composite numbers that are listed in a successive order.

Tips on Composite Numbers

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 predecessor-successor pair.
• 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

• PEMDAS
• Ordinal Numbers
• Co-prime Numbers
• Perfect Numbers
• Prime Numbers
• Integers
• Real Numbers
• Rational Numbers
• Irrational Numbers
• Complex Numbers
• Imaginary 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 and so on 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 that 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 predecessor-successor 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.

Find Two Consecutive Even Numbers whose Sum is 86.

Two consecutive even numbers can be listed if we assume one even number to be 2n, and the other is 2n + 2. Let us use the following steps to solve this.

• It is given that the sum of two consecutive even numbers is 86. So, we can write it as 2n + 2n + 2 = 86.
• Now, let us solve for the value of 'n', 4n + 2 = 86, this can be further solved as 4n = 84, so n = 21.
• Now, after substituting the value of n = 21, we get the two even numbers as follows. 2n = 2 × 21 = 42, so the first even number is 42 and the second even number is 2n + 2 = 42 + 2 = 44.
• Therefore, the two consecutive even numbers are 42 and 44 because their sum is 86. (42 + 44 = 86)

Are Two Consecutive Numbers Coprime?

Yes, any two consecutive numbers are always coprime numbers because they do not have any common factors other than 1, between them. We know that coprime numbers are pairs of numbers that do not have any common factor other than 1. For example, (6, 7), (78, 79), and (102, 103) are consecutive numbers that show that they are coprime and do not have any common factor other than 1.

What 3 Consecutive Numbers have a Sum of 126?

3 Consecutive numbers that have a sum of 126 are 41, 42, and 43. Let us understand this with the help of the following steps:

• Let the first consecutive number be 'n', the next number will be n + 1, and the third consecutive number will be n + 2.
• The sum of these 3 consecutive numbers is given as 126, so this can be written as n + n + 1 + n + 2 = 126.
• After solving this equation, we get, 3n + 3 = 126 and this gives, n = 41, so the next two numbers will be n + 1 = 41 + 1 = 42, and n + 2 = 41 + 2 = 43.
• Therefore, 3 Consecutive numbers that have a sum of 126 are 41, 42, and 43 because 41 + 42 + 43 = 126.