There are x people in the first row. If there is k+ 1 row, there are x+k students in k+ 1 row.

The summation formula is: (x+x+k) × (k+1) ÷ 2 =1000, that is, (2x+k)×(k+ 1)=2000.

Decomposition 2000, from k > 16 and k+ 1 > 17.

2000= 100×20=80×25=50×40=40×50=25×80=20× 100= 10×200=5×400=4×500=2× 1000= 1×2000

It is found that x=28 is a positive integer only when k+ 1=25, which is consistent with the meaning of the question.

So a student has 25 rows.