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The sequence (a[n]) satisfies a[1] = 3 and 

 

   a[n] = (a[n-1] − 1) / (a[n-1] + 1) 

 

for all n ≥ 2. Find a[100].

 

Anything in '[]' is meant to signify a subscript. Thanks in advance.

 Jun 1, 2021
 #1
avatar+121056 
+1

Let's see if  we  can find a pattern

 

The  terms  are

 

3  ,  2/4 ,  -1/3 ,   -2 ,     3

 

Note   that   the period will  repeat  after  every  4 terms

 

So      100/4  =   25    complete periods

 

So     a100  =   -2

 

cool cool cool

 Jun 1, 2021
edited by CPhill  Jun 1, 2021

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