Freeflows

Fibonacci Sequence Constants

The Fibonacci numbers are defined recursively by the equation \[ F_n = F_{n - 1} + F_{n - 2}\]for every integer $ n \ge 2 $, with initial values $ F_0 = 0 $ and $ F_1 = 1 $. Let $ G_n = F_{3n} $ be every third Fibonacci number. There are constants $ a $ and $ b $ such that every integer $ n \ge 2 $ satisfies \[ G_n = a G_{n - 1} + b G_{n - 2}.\]Find $ (a,b) $.

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$\frac{a}{b}$
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0
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$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

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$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$

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