The sequence a_n is defined by a_1 = 1, a_2 = 2, and
\(a_n = \dfrac{a_{n - 1}}{a_{n - 2}}\)
for all n >= 3. Find a_{2011}.
a1 = 1 a4 = 1 a7 = 1 a10 = 1
a2 = 2 a5 = ½ a8 = 2 a11 = ½
a3 = 2 a6 = ½ a9 = 2 a12 = ½
If this pattern holds, if you divide the index (the subscript) by 3 and get a remainder of 1, the value will be 1.
2011 = 670 x 3 + 1, so a2011 = 1
