# The sum of three consecutive odd numbers is 183. What is the smallest of the three numbers?

Dec 6, 2016

$59$

#### Explanation:

Of we consider the integers $0 , 1 , 2 , 3 , 4 , \ldots$ then a generic odd number would be represented as $2 n + 1$ where $n$ is an integer.

So the three consecutive numbers can be written as:

$2 n + 1 , 2 n + 3 , 2 n + 5$

So then:

$2 n + 1 + 2 n + 3 + 2 n + 5 = 183$
$\therefore 6 n + 9 = 183$
$\therefore 6 n = 174$
$\therefore n = 29 \implies 2 n + 1 = 59$

So the three numbers are: $59$, $61$ and $63$ whose sum is $183$