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 \(a_1+a_2+a_3+\cdots+a_{100}\).
$a_1 + a_2 + a_3 + \dots + a_{100} = \boxed{5}$
How did you get that?
I wrote a computer program, so I'm sure the answer is right.
