# The sum of three consecutive odd integers is 195, what are the integers ?

Feb 26, 2016

$63 , 65 , 67$

#### Explanation:

Say that there is some odd integer $x$. We don't know the value of it yet, we just know that $x$ is some odd integer.

The next consecutive odd integer would be $2$ away, or $x + 2$. The next would be $2$ after that, or $x + 4$.

Thus our three consecutive odd integers are $x , x + 2$ and $x + 4$.

Since we know their sum is $195$, we can say that

$x + \left(x + 2\right) + \left(x + 4\right) = 195$

Combine like terms and solve for $x$.

$3 x + 6 = 195$

$3 x = 189$

$x = 63$

Hence the other two odd numbers are $x + 2 = 65$ and $x + 4 = 67$.