# How do you find three consecutive even integers whose sum is 244?

Jun 13, 2015

There are no three consecutive even integers whose sum is 244.

Jun 13, 2015

To attempt to find three such integers, you could solve $244 = n + \left(n + 2\right) + \left(n + 4\right)$ and find that the resulting $n$ isn't an integer. So there are no such three consecutive even integers.

#### Explanation:

If there are three such integers then they are of the form $n$, $n + 2$ and $n + 4$.

Then we have:

$244 = n + \left(n + 2\right) + \left(n + 4\right) = 3 n + 6$

Subtract $6$ from both sides to get:

$238 = 3 n$

Divide both sides by $3$ to get:

$n = 79. \dot{3} \dot{3}$

which is not an integer, let alone an even one.

So there is no solution.