A word of advice, it is considered impolite and generally against forum rules to just bluntly solicit help without showing your own attempts. Documentation is very detailed and full of examples, for instance: ColorFunction. You should read about how to post properly.
So is this what you wanted?
ListPlot[seq, Joined -> True, Mesh -> Full, PlotStyle -> Thick,
ColorFunction -> Function[{x, y}, ColorData[{"Rainbow", "Reverse"}][x]]]

ListPlot[seq, Joined -> True, Mesh -> Full, PlotStyle -> Thick, Filling -> Bottom,
ColorFunction -> Function[{x, y}, ColorData[{"Rainbow", "Reverse"}][x]]]

Also the Demonstrations Project has a lot of free relevant examples, for instance:
DNA Rotator Walk
