Add your Google Apps Account on Apple iOS Devices

You can add your Google Apps account on your iphone or ipad to sync mail, contacts, tasks, calendars and notes.  Setup is quick and easy and should take less than 5 minutes.  All you’ll need to know is your Google Apps email address and password.  There is one ‘gotcha’ though – for best results you should NOT select the type of account as ‘Google’, use ‘Microsoft Exchange’ or ‘Corporate’ instead.

Add your Google apps account as follows:

Go to Settings > Mail, Contacts, Calendars > Add Account:

On the next screen select type of account = Exchange.  This will use the Microsoft Exchange Activesync protocol for seamless two-way sync of contacts, mail and calendars (‘Google Sync’):

Enter your email address, password and a descriptive name for this email account, then click ‘Next’:

iOS will now try and verify the settings for this account, and may ask for more information.  On the next screen you’ll have to enter the server ‘m.google.com’ and username (same as email address):

Once these details have been verified you can select what you would like to sync to your device:

And after you save the account it will appear in your list of mailboxes:

Reference: https://support.google.com/a/users/answer/138740?hl=en