The real farey sequence starts from 0/1 and end at 1/0 and we can get the median of this sequence by (0+1)/(1+0) which is 1/1. In this problem the sequence is 1/n to 1/1 and ascending order. So we can start a farey sequence by (1/n,1/1) then calculate (1/n, 1+1/n+1,1/1) but in this case we have to reduce the fraction in lowest form. But if we start creating sequence (1/0,1/1) then stop when the denominator will be greater then n. In this way we can create a feray sequence. Here the farey sequence for n=5 is,

0/1                                                         1/1

0/1                          1/2                           1/1

0/1               1/3      1/2        2/3               1/1

0/1       1/4   1/3 2/5 1/2  3/5  2/3  3/4        1/1

0/1 1/5 1/4   1/3 2/5 1/2  3/5  2/3  3/4  4/5  1/1

Now just leave 0/1 you got the sequence.