When solving word problems involving consecutive integers, it’s important to mental that we are looking for integers that room one unit apart.

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So if we have actually n as the first integer, then n + 1 will certainly be the 2nd integer, n + 2 will be the 3rd integer, n + 3 will be the fourth, n + 4 will be the fifth, and so on.


Let’s take for example: 15, left( 15 + 1 ight), left( 15 + 2 ight), left( 15 + 3 ight), left( 15 + 4 ight)

Our results come increase to: 15,,16,,17,,18,,19

When managing consecutive integers, notification that the difference in between the larger and smaller integers is constantly equal come 1.

Observe the following:

left( n + 1 ight) - left( n ight) = n + 1 - n = n - n + 1 = 1left( n + 2 ight) - left( n + 1 ight) = n + 2 - n - 1 = n - n + 2 - 1 = 1left( n + 3 ight) - left( n + 2 ight) = n + 3 - n - 3 = n - n + 3 - 2 = 1left( n + 4 ight) - left( n + 3 ight) = n + 4 - n - 3 = n - n + 4 - 3 = 1

Examples of resolving the amount of continually Integers

Example 1: The sum of 3 consecutive integers is 84. Uncover the 3 consecutive integers.

The an initial step to addressing word troubles is to uncover out what pieces of info are easily accessible to you.

For this problem, the following facts space given:

We need to include three integers that are consecutive The numbers are one unit apart from each various other Each number is one much more than the ahead numberThe sum of the continually integers is 84

With this facts in ~ hand, we can now collection up to stand for our 3 consecutive integers.

Let n be our an initial integer. Therefore,


We’re currently ready to create our equation. Mental that we are offered the sum, so we will be adding our 3 consecutive integers.


Let’s proceed and solve the equation.


Now the we have the worth for the change “n, we have the right to use this to identify the three consecutive integers.


Finally, let’s execute a quick check to make certain that the amount of the continually integers 27, 28, 29 is undoubtedly 84 as provided in our initial problem.

Example 2: uncover four continually integers whose sum is 238.

To start, let’s walk ahead and determine the necessary facts that are provided in this problem.

We will be adding four succeeding integers The surrounding integers are one unit apartThe amount of the 4 consecutive integers is 238

The following step is to stand for the 4 consecutive integers using the change “n“.

Let n it is in the first integer. Because the four integers space consecutive, this method that the second integer is the first integer enhanced by 1 or n + 1. In the same manner, the third integer can be stood for as n + 2 and the fourth integer together n + 3.

We have the right to then translate “the amount of four consecutive integers is 238” right into an equation.

Solve the equation:

Example 4: The sum of 3 consecutive integers is - ,90. What is the largest integer?

This a kind of trouble where you should be careful. Most of the time, us are only asked to discover the continuous integers which when added, must offer the mentioned sum. In this case, however, we no only have actually to find the three consecutive integers but likewise determine which amongst the three integers is the largest. Rule of thumb is to constantly read the trouble carefully and pay close fist to what is asked.

No matter exactly how straightforward a problem is, it’s still great practice to constantly identify what facts are obtainable to you. Think the these pieces of details as her compass showing you direction on just how to resolve the problem.

What we know:

We will be including three integers that are consecutive we should obtain a amount of - ,90 as soon as we include the 3 integersThe consecutive or adjacent integers only differ through one unitIt is likely that we will certainly be dealing with an adverse integers

Proceed through representing the consecutive integers.

Let extbf extitn, extbf extitn+1 and also extbf extitn+2 it is in the 3 consecutive integers.

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Now, let’s compose the equation by translating the math sentence, “the sum of 3 consecutive integers is - ,90” and also solve because that n.

Since n = - ,31, climate the 3 consecutive integers room - ,31, - ,30, and also - ,29.