Answer
Afterward, the central spot is bright.
Work Step by Step
If the Michelson interferometer produces a bright central spot, then the path length difference must be $~~n~\lambda~~$ for some integer $n$
If one mirror is moved forward $200~nm$, then this path length will decrease by a total of $400~nm$
If one mirror is moved back $200~nm$, then this path length will increase by a total of $400~nm$
The path length difference changes by a net of $800~nm$
Thus, the path length difference is still $n~\lambda$ for some integer $n$
Afterward, the central spot is bright.
