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Let \(a_1, a_2, a_3, \dots\)be  sequence of real numbers satisfying \(a_n = a_{n - 1} a_{n + 1}\)for all n>=2. If\(​​​​ a_1 = 1 + \sqrt{7}\), and \( a_{1776} = 13 + \sqrt{7},\) then determine\(a_{2009}.\)

 Feb 11, 2020
 #1
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a_{2009} is equal to 3 - 2*sqrt(7).

 Feb 11, 2020
 #2
avatar+29200 
+5

I get the following:

 

Edit:  Item number 3 in the list above should be a2/a1 not a2/a3 !

 Feb 11, 2020
edited by Alan  Feb 11, 2020

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