ParametricPlot[] is evaluated before the c's are replaced by numbers. You need to do the replacement first.
If f and r are scalars, then you're plotting a scalar, which ParametricPlot[] won't do.
If f and r are ordered pairs, then you're plotting an ordered pair, and you should see a plot, if the first point is addressed.
You can also use Unevaluated[] to address the first point:
Unevaluated[
ParametricPlot[Subscript[c, 1]*(0.95^k*{10, 7} . {f, r}) +
Subscript[c, 2]*(0.85^k*{2, 1} . {f, r}), {k, 1, 10}]] /.
{Subscript[c, 1] -> 1, Subscript[c, 2] -> 1, f -> {1, -1},
r -> {-3, 2}}
Oops, update: Just noticed the blackboard. I think one problem, which is addressed incorrectly in the 2nd and 3rd points, is that you should not be using . (Dot[]) in your code. The blackboard as scalar multiplication (* or Times[]), not vector-vector multiplication nor matrix-vector multiplication.
