[Boxxxed]

Options are O2-, N3-, F-


N3- is largest
I know the periodic trends so the question is do the positions in the periodic table have a larger effect than having an additional electron?

[JustinCh3m]

this question doesn't really concern itself with the trend that "radius increases from top left to bottom right of the Periodic Table."

Instead, realize that each of the 3 ions has a total of 10e-.  That being said, how many protons does each of the 3 ions have? 

The greater the # of protons, the greater the "pull" or "attraction" there will be on the "electron cloud".