Question

A sequence of numbers begins with 1, -1, -1, 1, -1. Each new number is found by taking the product of the
two preceding numbers. For instance the sixth number is the product of the fourth and fifth numbers. What is
the sum of the first 2013 numbers?

Answer 1

well, just look at the sequence: 1,-1,-1, 1,-1,-1, 1,-1,-1,...
You can see that it consists of groups of 3: 1,-1,-1
Each group has sum -1
2013 = 3*671
So the sum will be -671