Question 48
Let $\{a_{1}, a_{2}, a_{3}, \ldots\}$ be a sequence of real numbers such that for each $n \geq 1$,
$$
a_{n+2}=a_{n+1}+a_{n}
$$
Prove that for all $n \geq 2$, the quantity
$$
\left|a_{n}^{2}-a_{n-1} a_{n+1}\right|
$$
does not depend on $n$.
$$
a_{n+2}=a_{n+1}+a_{n}
$$
Prove that for all $n \geq 2$, the quantity
$$
\left|a_{n}^{2}-a_{n-1} a_{n+1}\right|
$$
does not depend on $n$.