I have no idea where you got this. There ARE "harmonic" progression (Tn= 1/n) and geometric progressions (Tn= a rn) but the example you give Tn = a + d(n-1) is neither one, it is an "arithmetic" progression.
Gauss worked with arithmetic-geometric progressions. I'm not sure what they "mean" but they have nice mathematical properties. When I get back to my books I'll post something on these. But arithmetic-harmonic I've never heard of.