I am trying to find the patterns but I don't see any.
8, 40/3, 152/9, 520/27, 1688/81 I know the denominator is 3^(n-1) *where n starts at 3
If you are really, really desperate you can always go to www.wolframalpha.com and just enter your list of numbers. This is what I got:
8, 40/3, 152/9,520/27,1688/81 - Wolfram|Alpha