# Three consecutive odd integers have a sum of 3. What are the numbers?

May 10, 2018

$\textcolor{b l u e}{- 1 , 1 , 3}$

#### Explanation:

Let $n$ be any integer:

Then $2 n$ is an even integer and $2 n + 1$ is an odd integer.

Three consecutive odd integers:

$\left(2 n + 1\right) + \left(2 n + 3\right) + \left(2 n + 5\right) = 3$

$6 n + 9 = 3$

$6 n = - 6$

$n = - 1$

The numbers are:

$2 \left(- 1\right) + 1 = - 1$

$2 \left(- 1\right) + 3 = 1$

$2 \left(- 1\right) + 5 = 3$