find the n th term of the series 5/2+20/13+10/9+20/23..... .

Answer 1

Just like in your previous problem, the corresponding AS is
2/5 + 13/20 + 9/10 + 23/20 + ...
= 8/20 + 13/20 + 18/20 + 23/20 + ...

looks like a = 8/20, and d = 5/20
or a = 2/5 and d = 1/4

so term(n) of this AS
= a + (n-1)d
= 2/5 +(1/4)(n-1)
= 2/5 + n/4 - 1/4
= n/4 + 3/20
= (5n + 3)/20

and finally the general term of the given HS
= 20/(5n+3)

Answer 2

20/5n+3