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Let

 

a_0=5

 

a_1=5

 

a_n=a_(n-1)+a_(n-2) for n>=2

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.

 Jun 22, 2021
 #1
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c = 4 + 4*sqrt(5)/5.

 Jun 23, 2021

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