Does the Voltage varies throughout a series circuit?

Short answer yes.

Suppose

R1 = 20 ohms

R2 = 30 ohms

R3 = 50 ohms

They are all connected in series and hooked to a 100v DC source.

The voltage across the 20 30 and 50 volt resistors will all be different.

If you mean can the 100v source vary. The answer to that is also yes, but a good steady output is usually what the manufactures come up with.