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The sequence \((a_n)\) is defined by \(a_1=a_2=1\)and 

\(a_{n + 2} = \begin{cases} a_n + a_{n + 1} \ \text{if $n$ is even,} \\ a_n - a_{n + 1} \ \text{if $n$ is odd.} \end{cases}\)

Compute \(a_1+a_2+a_3+\cdots+a_{100}\).

 Dec 20, 2021
 #1
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$a_1 + a_2 + a_3 + \dots + a_{100} = \boxed{5}$

 Dec 20, 2021
 #2
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How did you get that?

Guest Dec 20, 2021
 #3
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I wrote a computer program, so I'm sure the answer is right.

Guest Dec 20, 2021

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