# Question #6c321

Sep 21, 2016

$\left\{- 25 , - 23\right\}$

#### Explanation:

Any odd integer can be represented as $2 n + 1$, where $n$ is an integer. Suppose $2 n + 1$ is the lesser of the consecutive odd integers, then we have

$- 48 = \left(2 n + 1\right) + \left(2 n + 1\right) + 2$

$= 4 n + 4$

$= 4 \left(n + 1\right)$

$\implies n + 1 = - \frac{48}{4} = - 12$

$\implies n = - 13$

Thus, substituting in, we have the consecutive odd integers as

$2 n + 1 = 2 \left(- 13\right) + 1 = - 25$
and
$\left(2 n + 1\right) + 2 = - 25 + 2 = - 23$

Checking, $- 25 + - 23 = - 48$, as desired.