What are the next numbers of series - 2, 2.5, 3.33, 4.25, ? , ?

Question

In series 6,4,1,2,2,8,7,4,2,1,5,3,8,6,2,1,7,1,4,1,3,2,8,7,6, how many pairs of successive numbers have a difference of 1 each?

Answer 1

The sequence this series seems to follow is
1+5/(5*1),
2+5/(5*2),
3+5/(5*3),
4+5/(5*4)
So, next number will be 5+5/(5*5)=5.2
and so on...

Answer 2

It can also be written as
(2/1), (5/2), (10/3), (17/4) ......
Denominators are just 1,2,3,4,5 etc.,
But numerators are 2, 5, 10, 17 whose difference are 3, 5, 7
etc.,
So the next numerator must be 17+9 = 26
And hence by that format the next number is 26/5 = 5.2.