Programmable Unijunction transistors
I refer to my previous answers on this exercise:

Make electronics - charles pratt - experiment 11

PUT Base Resistors Question

The resistors aren't exactly in series; they're constructing a voltage divider, putting the PUT's base voltage at $$ 27/(15+27) * 6V $$
This is the programmable part of a PUT which sets the on voltage for it. In circuits 2 and 3 the gate is connected to the negative rail and is therefore at 0V, preventing it from ever turning on.

As in my other answers, PUTs are an unusual near-obsolete part and I wouldn't bother learning about them.