how do I find the input Z of a cascaded transmission line?

[seang]

Can I first find the input impedance relative to the segment nearest to the load, then use the found input impedance as the load in next iteration? Or can I add the characteristic impedances, since they are sort of in series?

[NoTime]

If you just hook different transmission lines together, then the impedance mismatches will cause reflections.
Any solution will be length and frequency dependent.

If you have matching networks between the segments then you can treat each segment independently.

[mdelisio]

Can I first find the input impedance relative to the segment nearest to the load, then use the found input impedance as the load in next iteration? Or can I add the characteristic impedances, since they are sort of in series?

Your first solution is correct. You cannot simply add the characteristic impedances.