Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
The problem is, You are using latest iOS 10 on your iPad but an old iTunes on your computer. You need iTunes 12.5 or later to work with iOS 10.
Are you using an Apple Mac or Windows PC ?
What version of Mac OS X are you using ? Click on the Apple icon and select About This Mac. You can see the version number there
The latest iTunes is 12.5 and it requires OS X 10.9 or later. You need to upgrade your Mac OS X 10.7 to latest version. The latest is 10.12 Sierra. This is your only way to fix this problem. The problem you are having is incompatibility issue with Mac and iPad version and there is no other way to make it work.
Follow the steps below to upgrade the OS X if your Mac support it.
Click on the Apple icon and App Store. This will bring App Store. Click Updates tab. If your Mac can handle latest OS X, then you will see macOS Sierra there with FREE UPGRADE button. Click Free Upgrade and enter your Apple ID and password.
This will download the update. It may take a few hours to download. Once the download is completed, it will bring the OS X Installer. Follow the onscreen instructions to install it. It may take up to 3 hours to install the upgrade.
I know you are looking for a solution, but this is your only way to fix this problem. If you are not satisfied, please don't rate me bad or poor or OK as it will badly affect my job here. You don't have to rate anything if you are not satisfied.
If you don't want to upgrade, then you have to sync your iPad with via iCloud with your Mac. You can use Dropbox application to transfer photos etc to your Mac.
On your iPad, go to Settings > iCloud and turn on all options. Then on Mac, go to System Preferences > iCloud and sign in to same account you used on your iPad. Then enable options to sync. This will sync stuffs via iCloud.
But this will not transfer contents from iTunes to iPad or vice versa.
Unfortunately, there is no way to downgrade now. Apple stopped the signing of iOS 9.3.5 last week. So it is not possible to downgrade now.
I'm sorry, I can only give you what the truth it and upgrading is the only solution. Please don't shoot the messenger if you are not satisfied
It was possible to downgrade to iOS 9.3.5 until Oct 19. See here --> http://appleinsider.com/articles/16/10/19/apple-stops-signing-ios-935-halting-any-downgrades-from-ios-10
You can sync Calendar, Contacts etc, with iCloud. To transfer documents and stuffs, you can use Dropbox or Google Drive.
The other work around is, get an external hard drive and install latest version of macOS on it. So you can use iPad with your Mac booting to that drive and you can switch this OS any time you want.