Question 11
The renaissance mathematician Leonardo da Pisa (better known as Fibonacci) is attributed to the sequence defined as follows $$
\begin{aligned}
& a_{1}=1 \\
& a_{2}=1 \\
& a_{i}=a_{i-1}+a_{i-2} \quad \text{ to } i\gt 2
\end{aligned}
$$ Express $a_{2 n}$ based only on the three terms $a_{n-1}$, $a_{n}$, $a_{n+1}$.
\begin{aligned}
& a_{1}=1 \\
& a_{2}=1 \\
& a_{i}=a_{i-1}+a_{i-2} \quad \text{ to } i\gt 2
\end{aligned}
$$ Express $a_{2 n}$ based only on the three terms $a_{n-1}$, $a_{n}$, $a_{n+1}$.