KöMaL 2018 B4962

Let $n$ be a positive integer. Solve the following simultaneous equations on the set of real numbers: $a_1^2 + a_1 - 1 = a_2$ $a_2^2 + a_2 - 1 = a_3$ $\vdots$ $a_n^2 + a_n - 1 = a_1.$