ipad compatibility with router extender

I have the regular wi-fi ipad and an N router. Things are fine until I want to extend the distance from the router to the ipad (from my upstairs office in the front of the house to my back yard).

With this type of ipad I have been told an N type extender won't work. Is this true? I'm afraid if I go back to a G router I will screw things up (and I'm pretty sure I can't add a second router without creating issues). How come the ipad works well with an N router but won't work with an N extender?