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The sequence a_n satisfies a_0 = 1, a_1 = -1, and \(a_i = a_{i - 1} + 2a_{i - 2}\) for i >= 2.  Find a_{100}.

 Oct 10, 2022
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a(0)==1

a(1) == -1

a(2)== - 1 + 2*1 ==1

a(3)==1 + 2*- 1 ==-1

a(4)== - 1 + 2*1 == 1

a(5)==1 + 2*- 1 == - 1........and so on

 

Then the sequence is: 1,  - 1,  1,  - 1,  1,  - 1.........etc.

 

All EVEN terms end in 1 and all ODD terms end in - 1

So: a(100)== - 1 + 2*1 ==1

 Oct 10, 2022

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