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Hi Tim - the iPad, HDMI adapter, & a HDTV are not always compatible bedmates, unfortunately; this is an oft asked question and a search would likely provide plenty of hits of past suggestions & solutions - e.g. one HERE.
First, keep in mind that the output of the iPad is a 4:3 (1.33) aspect ratio and that of a modern HDTV 16:9 (1.78), so w/o distortion adjustments, the screen of the iPad on the TV will have side bars (same as watching an old 4:3 movie). Second, the application/video source likely impacts on your options of 'filling' your TV screen (upscaling being one possibility) - now, you can check the features w/i an app & the iPad settings, in addition to the choices on your HDTV (e.g. zooming, changing the aspect ratio, etc.) - there seems to be no perfect solution using the HDMI cable.
Another choice is to use an Apple TV - don't own one myself (have a Roku device which streams movies & TV shows fully to my HDTV if in that format), but hopefully others will 'chime in' w/ more advice - good luck! Dave