# How do you find a set of three consecutive integers whose sum is equal to the sum of the next two consecutive integers immediately following them?

May 20, 2016

$\left\{4 , 5 , 6\right\}$

#### Explanation:

Let $x$ be the least of the first three integers. Then the set consists of $\left\{x , x + 1 , x + 2\right\}$ where

$x + \left(x + 1\right) + \left(x + 2\right) = \left(x + 3\right) + \left(x + 4\right)$

Solving for $x$:

$x + \left(x + 1\right) + \left(x + 2\right) = \left(x + 3\right) + \left(x + 4\right)$

$\implies 3 x + 3 = 2 x + 7$

$\implies 3 x - 2 x = 7 - 3$

$\therefore x = 4$

Checking our result:

$4 + 5 + 6 = 15 = 7 + 8$

Thus, we have our answer as $\left\{4 , 5 , 6\right\}$