[Note: You must use different letters, because the question with n's
in both places does not make any sense.  That's why I changed it to
the first k terms instead of the first n terms]

The A.P. whose nth term is 2n+5 is 7,9,11,13,15,17,...

The median of the first 1 term is 7
The median of the first 2 terms is 8
The median of the first 3 terms is 9
The median of the first 4 terms is 10
The median of the first 5 terms is 11
The median of the first 6 terms is 12

So the sequence of medians of the first k terms of the A.P above
is the A.P. 7,8,9,10,11,12

The kth term of that is k + 6

Edwin