Different sequences

Compare the following list of circles which are generated by different ways of defining the sequence of dilation factor. Based on a given ratio r, dilation factors in the 2 cases are: r, r, r, r, r, … and r, 2r, 3r, 4r, 5r, ... You can click the lower left animation button or drag the slider to change the value of r.
The command is Sequence[Dilate[c, r^n, O], n, 1, 10] where c is the name of the circle.
In this case, the command is Sequence[Dilate[c, r*n, O], n, 1, 10]
Can you vary the dilation factors in some other ways making use of different algebraic expressions?