Number Sequence

[markwh]

What are the next 2 in this sequence - preferably with an explanation as to why.

1/5, 1/4, 1/3, 2/5, 1/2, 3/5

Many thanks in anticipation.

I have a possible answer (which I will reveal in due course, rather than colour anybody's judgement), but cannot put an explanation to it.

[markwh]

Apologies to anybody who worked on this from the "summary page".

For some reason, the dividing line of (what I believe are) fractions does not show up there!

Mark.

[gen2]

This is the Farey series of order 5.
The complete sequence is as follows:

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

Googling for "Farey series" will give many pages of explanation.