I have just recently bought the Nikon D7200 and am having trouble using aperture priority mode. I have been doing exactly what the manual says - I switch the mode to A but when I turn the dial on the right the F stop does not change. Even when I have the info screen up the shutter speed number flashes but the F stop still doesn't budge.
The D7200 has two control dials. Which one are you using to try and change the aperture setting? The one on the back of the camera controls shutter speed. The one just in front of the shutter button controls aperture. This is different from lower tier Nikon cameras that have only one control wheel.
If the aperture value will not move in only one direction, but will move in the other, then you are probably bumping up against a limit you have imposed using another setting, such as minimum shutter speed. By flashing the shutter speed in the info screen it is telling you any further change in aperture in that direction will result in the need for a slower shutter speed than has been set by you for minimum shutter speed. In that case you need to disable the option that limits the minimum shutter speed (or also enable an option that allows for raising the ISO automatically to compensate for the narrower aperture).
Do you have a flash enabled and are you are trying to open up the aperture to a setting that would require the shutter speed to be shorter in duration than the camera's flash sync speed? If the shutter speed flashing on the info screen is the camera's sync speed then you need to either enable Auto FP if you have a flash capable of AFP (Nikon's name for high speed sync flash) or reduce the ISO setting to allow for a wider aperture with the sync speed. If you are already at minimum ISO, then a neutral density filter would be the next option.