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Let

 

\(\begin{align*} A_0 &= 6 \\ A_1 &= 5 \\ A_n &= A_{n - 1} + A_{n - 2} \; \textrm{for} \; n \geq 2. \end{align*}\)


There is a unique ordered pair (c, d) such that \(c\phi^n + d\widehat{\phi}^n\) is the closed form for sequence \(A_n\).

Find c using the Fibonacci and Lucas number sequences.

 Apr 10, 2021
 #1
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c = 1 + sqrt(5)/5

 Apr 10, 2021

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