If the $99 Apple TV is too expensive (or overkill), grab a ~ $50 dock connector from Apple. There are 30 pin and Lightning versions, each compatible with the specific respective models. YMMV. See here for a cheaper one, which may be worth trying if you are on a budget. I have not had as much luck with the cheaper generics, even 'Apple certified' models, such as this one-
http://www.amazon.com/Apple-I-Pad-Dock-30-Pin-Adapter-White/dp/B0052E4SXY/ref=sr_1_1?s=wireless&ie=UTF8&qid=1423669503&sr=1-1&keywords=apple+30+pin+to+HDMI
Just buy it from a seller with a liberal return policy, and you should be good to go.
Is it possible to use HDMI to USB to connect monitor with iPad?
I know I can use HDMI to USB connect a monitor with a computer, but how about use this way to connect iPad?

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