The next thing to do is add on -3, which is the same as subtracting 3, to get back to 3 once more.
This pattern continues on forever. To ensure you add on either +3 or -3 to the previous term, we add on the general term 3*(-1)^n
Overall, the nth term is found by a(n) = a(n-1) + 3*(-1)^n, which is what choice C shows. I'm assuming your teacher meant to write 3(-1)^n instead of 3(-1)n