I cannot get airplay to work with my Apple TV 3. I reset the Apple TV but the version number is only 7.7. It will not update to any newer number. My iPad does not see the Apple TV either

my Apple TV 3. I reset the Apple TV but the version number is only 7.7. It will not update to any newer number.

This is as expected. Version 7.7 is the latest version system software for the Apple TV (3rd generation). About Apple TV (2nd and 3rd generation) software updates - Apple Support

I cannot get airplay to work. My iPad does not see the Apple TV

Learn how to use AirPlay from Use AirPlay to stream video or mirror the screen of your iPhone, iPad, or iPod touch - Apple Support

Learn troubleshooting any issues from If AirPlay or screen mirroring isn’t working on your device - Apple Support

What type of content (streaming service/app) were you trying to mirror? Not all support AirPlay.