"Google supports Google Sync (and the Exchange ActiveSync protocol) for Google Apps for Business, Government, and Education. Only these users can set up a new Google Sync connection that uses Exchange ActiveSync."
Use the Gmail Exchange ActiveSync server settings for accessing Gmail accounts in Exchange-enabled email programs.
www.lifewire.com
You do know that Google has purposely broken Gmail "exchange"for "normal" users because they don't want to pay Microsoft for the Active sync license right? The only way to have full Gmail functionality on your iPhone is to download the Gmail app. Hence (OK one of the many) reasons that I do not use Gmail on my phone. Or frankly at all.