Thank you Andrei for this explanation (Andrei Lazanu, School 205, Bucharest)

I observe that, after writing the first Farey Sequence, the next one could be calculating by writing a mediant. Then, the next ones in the same matter, so this method works for all the Farey Sequences. It works for all the terms of the sequence and you know sure that you haven't missed one term. Now, I write all the terms up to the 10 ^th :

I use the same method for all the other Farey Sequences: