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102
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avatar+146 

The sequence \((a_n)\) is defined by \(a_0=2, a_1=1\)  and \(a_n=a_{n-1}\sqrt{3}-a_{n-2}\)
for all \(n\geq2\) Find \(a_{100}\).

 

Thanks in advance.

 Jul 21, 2020
 #1
avatar+21957 
0

If you use the rules of the sequence, you will get the first six elements to be unique elements.

 

When you continue the sequence, you will find that:

     a6  =  -ao     a7  =  -a1     a8  =  - a2     a9  =  -a3     a10  =  -  a4     a11  =  -a5 

 

Continuing, you find that:

     a12  =  a0     a13  =  a1     a14  = a2     ...

 

Etc.

 

Knowing this, can you calculate the value of a100?

 Jul 21, 2020

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