# What is the sum of three consecutive even integers is -360?

If you are trying to find the three numbers, they are $- 122$, $- 120$, and $- 118$.

#### Explanation:

They are consecutive, so the average would be $- \frac{360}{3} = - 120$. That would give you $- 120$, $- 120$, and $- 120$.
However, they are consecutive even integers. So subtract 2 from one of the numbers and add 2 because it will even out the average. That should get $- 122$, $- 120$, and $- 118$.

May 24, 2018

-118,-120,-122

#### Explanation:

Considering that the numbers have to be consecutive, the three numbers would be close in value to each other. we'd be looking for numbers that are close to:

$- \frac{360}{3} = \textcolor{b l u e}{- 120}$

So we need 3 consecutive numbers that are close to 120, and sum to 360. Luckily 120 can be considered an element in the 3-number set:

$- \textcolor{b l u e}{120} - 122 - 124 = \textcolor{red}{- 366}$

$- 116 - 118 - \textcolor{b l u e}{120} = \textcolor{red}{- 354}$

$- 118 - \textcolor{b l u e}{120} - 122 = \textcolor{g r e e n}{- 360}$

So now we have our set:

$\left\{- 118 , - 120 , - 122\right\}$