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Variations of Consecutive Integer World Problems

More than 2 consecutive integers

Sometimes you will encounter a problem which has more than two consecutive numbers, such as the one below.

When added, four consecutive numbers have a sum of 18. What are the numbers?

You can solve this much like the previous problem. The difference is that you will have to define four numbers (instead of two), like we did below. Note: each consecutive number is found by adding 1 to the previous number.

Let x = The First Consecutive Number
Let x + 1 = The Second Consecutive Number
Let x + 2 = The Third Consecutive Number
Let x + 3 = The Fourth Consecutive Number

Your equation will look like this.

x + (x + 1) + (x + 2) + (x + 3) = 18

Negative consecutive integers

To solve problems which involve negative consecutive numbers, it is important that you ignore the negative sign, and that you do not do anything differently.

The sum of two consecutive integers is -9. What are the integers?

Keep the variable x positive, as shown, so that the answer does not come out wrong.

Let x = The First Consecutive Number
Let x + 1 = The Second Consecutive Number

Thus the equation will have the form

x + (x + 1) = -9

Even or Odd Consecutive Numbers

The only difference between ordinary consecutive numbers and even or odd consecutive numbers is the space between each number. The next consecutive number after 16 can be found by adding 1. The next consecutive even number can be found by adding 2. Similarly, the next consecutive odd number after 7 is 7 + 2, or 9.

Examine this problem

Two consecutive even numbers have a sum of 30. What are the numbers?

Since each even number is 2 away from the next, it is logical that you should define each number like the following

Let x = The First Consecutive Even Number
Let x + 2 = The Second Consecutive Even Number

Leading to the equation

x + (x + 2) = 30

The final page links to various resources which can aid you in your study of this lesson.


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