I have five pairs of balls, with each pair being a different color. If two balls of the same color are compared on a balance scale they will balance. Conversely if two balls of different color are compared on a balance scale they will not balance. I also know that the five weights of the balls are in an arithmetic sequence.

With the given information about the balls, devise a strategy to sort the balls into ascending order by weight using only a balance scale at most six times.