The correct option is the last:
[tex] a_n = -2a_{n-1}+1 [/tex]
In fact, every term in the sequence is one more than twice the opposite of the previous one:
We start with 3. Twice its opposite is -6. Plus one, we get -5.
We start with -5. Twice its opposite is 10. Plus one, we get 11.
We start with 11. Twice its opposite is -22. Plus one, we get -21.
