Three consecutive intergers have a sum of 54. find the integers

Let's take a look at three very familiar consecutive integers before we get more abstract with it: 1, 2, and 3. How do 2 and 3 relate to 1? Well, 2, is 1 + 1, and 3 is 1 + 2. If we look at that integers 5, 6, and 7, we see a similar pattern; 6 is 5 + 1, and 7 is 5 + 2. In general, if we want to look at any 3 consecutive integers starting with some integer , the following integers will be  and .

We want to find 3 consecutive integers that add up to 54, so we'll need to add , , and  together, set their sum equal to 54, and solve for  to find them.



Combining like terms on the left side:



And solving for :



The first of the three consecutive integers is 17, which means the next two must be 18 and 19. Checking our work, we find that indeed:



Our three integers are 17, 18, and 19.