Question

The sum of three consecutive odd numbers is 51

Answer 1

Tried a whole bunch of odd sequences:

11 + 13 + 15 = 39
Nope too small.

21 + 23 + 25 = 69
Woah too big!

And after a few more trials found that:
17 + 19 + 21 = 51

Woohoo!

Answer 2

An odd number is ussualy written as "2k+1" and an even number is written as "2k".
Now, as there are 3 consecutive odd numbers that sum to 51, it can be written this way: 
(2k+1)+(2k+3)+(2k+5)=51
6k+9=51
6k=42
k=7 => The numbers are: 2*7+1=15
                                         2*7+3=17
                                          2*7+5=19
15+17+19=51