Question 77
A sequence of real numbers $a_{1}, a_{2}, \ldots$ satisfies the relation
$$
a_{n} = -\max_{i+j=n} (a_{i} + a_{j}) \quad \text{ for all } n \gt 2017
$$
Prove that this sequence is bounded, i.e., there is a constant $M$ such that $|a_{n}| \leqslant M$ for all positive integers $n$.
$$
a_{n} = -\max_{i+j=n} (a_{i} + a_{j}) \quad \text{ for all } n \gt 2017
$$
Prove that this sequence is bounded, i.e., there is a constant $M$ such that $|a_{n}| \leqslant M$ for all positive integers $n$.