Given the sequence a_1 = 1, a_2 = 2, and \(a_n = a_{n - 1} - a_{n - 2}\) for all n > 2, find the sum of the first 100 terms.
+23246 Let's find a pattern: an = an - 1 - an - 2
a1 = 1 a7 = -1 - -2 = 1 a13 = -1 - -2 = 1
a2 = 2 a8 = 1 - -1 = 2 etc.
a3 = 2 - 1 = 1 a9 = 2 - 1 = 1
a4 = 1 - 2 = 1 a10 = 1 - 2 = 1
a5 = -1 -1 = -2 a11 = -1 -1 = -2
a6 = -2 - -1 = -1 a12 = -2 - -1 = -1
Also notice that the sum of a1 through a6 is 0.
The first 16 groups -- a1 through a96 have a sum of zero.
So, we just need to add the first 4 terms in the next group of 6 ...
Can you finish it?
