SOLUTION: pattern:1/2;2/5;6/8;8/11 write down the next two terms of the pattern and determine the general term

Here are what I think are the first 10 terms:

1/2, 2/5, 6/8, 8/11, 15/14, 18/17, 28/20, 32/23, 45/26, 50/29,

The numerators 1, 2, 6, 8, 15, 18, 28, 32, 45, 50

follow this pattern:

1∙1, 2∙1, 3∙2, 4∙2, 5∙3, 6∙3, 7∙4, 8∙4, 9∙5, 10∙5,

The first factor of the numerators are just 1, 2, 3,...
with the general term of simply n.

The second factors of the numerators are
1, 1, 2, 2, 3, 3, 4, 4, 5, 5,
The way to get the general term is by using the greatest integer
function, also called the floor function of (n+1)/2 
indicated by ë(n+1)/2û, the greatest integer not exceeding (n+1)/2

The denominators are 2,5,8,11,14,17,... with general term 3n-1

So the general (nth) term is: 

an = n∙ë(n+1)/2û/(3n-1).

Edwin