Question 25
Let $a_1, a_2, \dots, a_n$ ($n \ge 4$) be positive real numbers with $a_1 \lt a_2 \lt \dots \lt a_n$. For any positive real number $r$, the number of ternary groups $(i, j, k)$ satisfying $\frac{a_j - a_i}{a_k - a_j} = r$ ($1 \le i \lt j \lt k \le n$) is denoted as $f_n(r)$. Prove $f_n(r) \lt \frac{n^2}{4}$.