When solving word problems involving continuous integers, it’s necessary to psychic that we are searching for integers that space one unit apart.
You are watching: The sum of three consecutive integers is
So if we have actually n together the very first integer, climate n + 1 will certainly be the 2nd integer, n + 2 will be the third integer, n + 3 will certainly be the fourth, n + 4 will certainly 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 outcomes come up to: 15,,16,,17,,18,,19
When taking care of consecutive integers, an alert that the difference in between the larger and also smaller integers is always 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 fixing the amount of consecutive Integers
Example 1: The sum of 3 consecutive integers is 84. Find the three consecutive integers.
The an initial step to fixing word troubles is to uncover out what piece of information are obtainable to you.
For this problem, the following facts room given:We need to include three integers that space consecutive The numbers space one unit except each other Each number is one an ext than the vault numberThe sum of the consecutive integers is 84
With this facts in ~ hand, we deserve to now set up to stand for our 3 consecutive integers.
Let n it is in our very first integer. Therefore,
We’re now ready to write our equation. Mental that we are given the sum, therefore we will certainly be including our 3 consecutive integers.
Let’s proceed and solve the equation.
Now that we have the value for the variable “n, we can use this to determine the three consecutive integers.
Finally, let’s execute a quick check to make sure that the amount of the continuous integers 27, 28, 29 is undoubtedly 84 as provided in our initial problem.
Example 2: find four continuous integers whose sum is 238.
To start, let’s walk ahead and determine the important facts that are provided in this problem.We will be adding four succeeding integers The adjacent integers space one unit apartThe amount of the four consecutive integers is 238
The following step is to stand for the 4 consecutive integers making use of the change “n“.
Let n be the first integer. Due to the fact that the four integers room consecutive, this method that the second integer is the first integer enhanced by 1 or n + 1. In the very same manner, the third integer have the right to be represented as n + 2 and the fourth integer as n + 3.
We deserve to then analyze “the amount of four consecutive integers is 238” into an equation.
Solve the equation:
Example 4: The amount of 3 consecutive integers is - ,90. What is the largest integer?
This a form of difficulty where you should be careful. Many of the time, us are just asked to discover the continuous integers which as soon as added, must give the stated sum. In this case, however, we no only have actually to uncover the three consecutive integers but additionally determine which amongst the three integers is the largest. Dominance of thumb is to always read the difficulty carefully and pay close fist to what is asked.
No matter just how straightforward a problem is, it’s still great practice to always identify what truth are obtainable to you. Think of these piece of information as your compass mirroring you direction on how to fix the problem.
What us know:We will certainly be adding three integers that room consecutive we should get a sum of - ,90 once we include the three integersThe continually or adjacent integers just differ through one unitIt is most likely that we will certainly be dealing with an unfavorable integers
Proceed through representing the continuous integers.
Let extbf extitn, extbf extitn+1 and also extbf extitn+2 be the three consecutive integers.
See more: Br A Heterogeneous Society Is Made Up Of _____., A Heterogeneous Society Is Made Up Of _____
Now, let’s write the equation by translating the mathematics sentence, “the amount of three consecutive integers is - ,90” and solve for n.
Since n = - ,31, then the three consecutive integers space - ,31, - ,30, and - ,29.