Consecutive numbers are numbers that, when counting, follow each other and are in order. For example: 1, 2, 3, 4…, or 59, 58, 57, 56… We can also divide them between consecutive even numbers and consecutive odd numbers.

## What are consecutive numbers

As mentioned before, consecutive numbers are numbers that follow each other in order without jumping. In addition to consecutive numbers that vary by one unit, consecutive numbers can also be even or odd.

### How to get a consecutive number

To obtain a consecutive number, one unit must be added to the previous number. That is, using this equation:

**number: n**

**Consecutive number = n + 1.**

“n” can be any integer. For example: To find out what the consecutive number of 185 is, we add 1 to it and we get 186.

### Consecutive even numbers

To obtain a consecutive even number, two units must be added to the previous even number. This can be expressed with the following equation:

**Even number: 2 . no**

**Consecutive even number = 2 · n + 2**

Here too “n” can be any integer. For example, some consecutive even numbers are: 8 and 10 (if n=4), or 46 and 48 (if n=23).

### Consecutive odd numbers

A consecutive odd number can be obtained by adding two units to the previous odd number. You can use the equation:

**Odd number: 2 n – 1**

**Consecutive odd number = (2 · n − 1) + 2**

In this case “n” is also any integer. Some examples of consecutive odd numbers are 1 and 3 (for n=1), or 77 and 79 (for n=39).

## consecutive multiples

Math problems are often based on properties of consecutive odd or even numbers. Or also in consecutive numbers that are increasing in multiples of three, such as 3, 6, 9, 12. In this example, the numbers 3, 6, 9 are not consecutive numbers, but consecutive multiples of 3. In other cases, the problems are about consecutive even numbers (2, 4, 6, 8) or consecutive odd numbers (7, 9, 11). Here you take an even number and then the next even number, or else an odd number and the next odd number.

If “x” is one of the numbers, the algebraic representation of the consecutive numbers would be: x + 1, x + 2, x + 3…

If the problem to solve is about consecutive even numbers, it is important that the first number you choose is even. To do this, the first number must be 2.x instead of x. But keep in mind that the next consecutive even number is not 2x + 1 (because this would give an odd number), but 2x + 2, 2x + 4, 2x + 6, and so on.

Similarly, consecutive odd numbers would be expressed: 2x + 1, 2x + 3, 2x + 5…

## Math problems with consecutive numbers

Here are two math problems to practice consecutive numbers:

**Example 1:**

Suppose the sum of two consecutive numbers is 15. What would those numbers be?

To solve this problem we have to consider that given any number, let’s call it “x”, its consecutive number will be x+1. Therefore, the sum between x and x+1 must be equal to 23. We put this in an equation and solve:

**Equation** :

x + (x + 1) = 23

2x + 1 = 23

2x = 22

x=11

So, your numbers are 11 (value of x) and 12 (value of x+1).

**Example 2:**

Now imagine that in the previous example we had chosen the consecutive numbers differently: for example, that the first number was x -3 and the second number was x -4 (note that these numbers are still consecutive numbers: one comes directly after the first). other). Do you get the same consecutive numbers?

To solve this problem we follow the same reasoning as in the previous case: the sum of the two consecutive numbers must be equal to 23.

**Equation** :

(x – 3) + (x – 4) = 23

2x – 7 = 23

2x = 30

x = 15

Here you can see that x is equal to 15, while in the previous problem, x was equal to 11. However, the value of x is only used to calculate the consecutive numbers, it is not necessarily one of the consecutive numbers. To determine the consecutive numbers we substitute the value of x in the expression we use to define each number: x – 3 and x – 4.

- 15 – 3 = 12
- 15 – 4 = 11

As you can see, it has the same answer as in the previous problem.

It may be easier if you choose different variables for your consecutive numbers. For example, if you have to solve a problem involving the product of five consecutive numbers, you can calculate it using either of the following two methods:

**x (x + 1) (x + 2) (x + 3) (x + 4)** or

**(x – 2) (x – 1) (x) (x + 1) (x + 2)**

As you can see, the second equation is easier to calculate since it can take advantage of the properties of the difference of squares.

**Exercises to practice consecutive numbers**

Here are more consecutive number exercises. Try to solve them with the methods taught above.

- What are the five consecutive numbers whose total sum is zero?
- Solution= -2, -1, 0, 1, 2

- What are the two consecutive odd numbers that have a product of 143.
- Solution= 11, 13

- There are four consecutive even numbers that add up to 148. What are those numbers?
- Solution= 34, 36, 38, 40

- What are the three consecutive multiples of six that add up to 126?
- Solution= 36, 42, 48

- If the sum of four consecutive integers is 54, what are those numbers?
- Solution= 12, 13, 14, 15

- The sum of five consecutive even integers is 110. What are those numbers?
- Solution= 18, 20, 22, 24, 26

- What are the two consecutive numbers whose product is 600. What are those numbers?
- Solution= 24, 25

- If you do a subtraction between the product of two consecutive numbers and the sum of the same two numbers, the result is 19. What are those numbers?
- Solution= -4 and -3 or 5 and 6

### Bibliography

- López Mateos, M.
*Basic Mathematics.*(2017). Spain. CreateSpace. - dk.
*The math book.*(2020). Spain. dk.