Let there be $n$ such trips. Call a student who participated in less that $\frac{n}{17}$ trips lazy and assume that there are $k$ such students. If there would not exist a field trip without a lazy student, we would have $k\cdot\frac{n}{17} >n$ and so $k\geq 18$. However, then there would be at most $2n+18\cdot \frac{n}{17}< 4n$ participations, which is a contradiction.