My first question is whether this is an arith. sequence or a geom. sequence.
Assuming that it's geom., let's find the multiplier of 5/6 that produces 5/9:
5/9
---- = 6/9 = 2/3
5/6
Next, check whether (2/3)(5/6) actually produces 5/9: 10/18 = 5/9 (yes).
The next step is to determine whether 2/3 times 5/9 produces 10/27:
2 5
-- * --- = 10/27 Yes.
3 9
So, it appears that you have a geometric sequence with first term 5/6 and common ratio 2/3.
To find the next term of the sequence, multiply the last given term (20/81)by the common ratio (2/3); we get 20*2
-------- = ??
3(81)