A harmonic sequence is a sequence of the reciprocals of the terms of an
arithmetic sequence.  Therefore we look at the arithmetic sequence

2/3, 2/1, 10/3, 14/3,...

2/1-2/3 = 6/3-2/3 = 4/3
10/3-2/1 = 10/3-6/3 = 4/3
14/3-10/3 = 4/3

So we add common difference 4/3 successively until we have
9 terms:

14/3+4/3 = 18/3 = 6/1
 6/1+4/3 = 18/3+4/3 = 22/3
22/3+4/3 = 26/3
26/3+4/3 = 30/3 = 10/1
10/1+4/3 = 30/3+4/3 = 34/3

2/3, 2/1, 10/3, 14/3, 6, 22/3, 26/3, 10/1, 34/3

That's the arithmetic sequence of reciprocals of the harmonic
sequence.  So the harmonic sequence is the sequence of
reciprocals of the arithmetic sequence:

3/2, 1/2, 3/10, 3/14, 1/6, 3/22, 3/26, 1/10, 3/34

Edwin