Answer:
The third number in this sequence is 63.
Step-by-step explanation:
Let the first odd number be <em>x</em>.
Since our sequence are consecutive odd numbers, the second term must be (<em>x</em> + 2) and the third (<em>x</em> + 4). If we only add one, we will get even numbers.
Their sum is 183. Hence:
![x+(x+2)+(x+4)=183](https://tex.z-dn.net/?f=x%2B%28x%2B2%29%2B%28x%2B4%29%3D183)
Solve for <em>x</em>. Combine like terms:
![3x+6=183](https://tex.z-dn.net/?f=3x%2B6%3D183)
Subtract six from both sides:
![3x=177](https://tex.z-dn.net/?f=3x%3D177)
And divide both sides by three. Hence:
![x=59](https://tex.z-dn.net/?f=x%3D59)
Therefore, our sequence is 59, 61, and 63.
The third number in this sequence is 63.
Note: If we do not get an odd number or if we get a fraction for <em>x</em>, we can conclude that no three consecutive integers sum to 183.