Question 131
Let $n \ge 2$ be an integer. Find the largest real number $\lambda$ such that the inequality
$$
a_n^2 \ge \lambda(a_1 + a_2 + \cdots + a_{n-1}) + 2a_n
$$
holds for any positive integers $a_1, a_2, \dots, a_n$ satisfying $a_1 \lt a_2 \lt \dots \lt a_n$.
$$
a_n^2 \ge \lambda(a_1 + a_2 + \cdots + a_{n-1}) + 2a_n
$$
holds for any positive integers $a_1, a_2, \dots, a_n$ satisfying $a_1 \lt a_2 \lt \dots \lt a_n$.