An number is a number divisible by
2.
Therefore, any even number can be represented by the expression
2n, where
n is some . Let's take a look at some examples.
61636=2⋅3=2⋅8=2⋅18
Since even and numbers alternate, two consecutive even numbers are at a distance of
2 from one another. If the first of the three consecutive even integers is
2n, then the next two are larger by
2 from the one before. We can write that down.
2n ⟶+2 2n+2 ⟶+2 2n+4
To find the three consecutive even integers whose sum is
54, we need to solve the following .
2n+(2n+2)+(2n+4)=54
Let's add together these three and then isolate
n.
2n+(2n+2)+(2n+4)=54
2n+2n+2+2n+4=54
6n+6=64
6n=48
n=8
Let's recall that the three numbers are
2n, 2n+2, and
2n+4. If we now substitute
8 for
n in those expressions, we will have three consecutive even numbers whose sum equals
54. Let's do it.
2(8)2(8)+22(8)+4=16=18=20