VTMO 2026 - Grade 9 - Semifinal - SET 1 - Self-study Question 9

Let $A=\{a_1,a_2,\ldots,a_{11}\}$ consist of positive integers with $a_i<a_j$ whenever $i<j$. For every positive integer $n\le2024$ not in A, some distinct elements of A have sum n. Find the smallest possible value of $a_{10}$.