MathNet 1962 — Part 01 Question 6

Given $a_0$, $a_1$, ..., $a_n$, satisfying $a_0 = a_n = 0$, and $a_{k - 1} - 2a_k + a_{k + 1} \geq 0$ for $k = 1, 2, ..., n-1$. Prove that all the numbers are negative or zero.