RU-ALLRUSSIAN 1962 Problem 13

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