Question 26
Determine all real numbers $A$ such that every sequence of non-zero real numbers $x_{1}, x_{2}, \ldots$ satisfying
$$
x_{n+1}=A-\frac{1}{x_{n}}
$$
for every integer $n \geqslant 1$, has only finitely many negative terms.
$$
x_{n+1}=A-\frac{1}{x_{n}}
$$
for every integer $n \geqslant 1$, has only finitely many negative terms.