ITOT 45 Spring 2024 · THPT · O (Basic) Question 1

A sequence of real numbers$a_1,a_2,\ldots$ satisfies$a_{n+2}=(a_n+a_{n+1})/2$ for every$n\ge1$. Prove that all parabolas$y=x^2+a_nx+a_{n+1}$ have a common point.