# The sum of three consecutive odd integers is 45, how do you find the numbers?

Mar 4, 2016

13, 15, 17

#### Explanation:

Consider three consecutive odd integers $\left(2 n - 1\right) , \left(2 n + 1\right) , \left(2 n + 3\right)$
Where n is Integer.

If the sum of these odd integers is 45,
Then: $\left(2 n - 1\right) + \left(2 n + 1\right) + \left(2 n + 3\right) = 45$
$6 n + 3 = 45$
$6 n = 42$
$n = 7$

Substituting $n = 7$ into $\left(2 n - 1\right) , \left(2 n + 1\right) , \left(2 n + 3\right)$
Gives 13, 15, 17

To check: $13 + 15 + 17 = 45$