How to install iOS 7 from beta 6 and GM?

This year was my first time experimenting with iOS betas. Since earlier today, I've been trying to update my iPhone 5 and iPad Mini from iOS 7 beta 6 (on my iPhone 5), and the iOS 7 GM (on my iPad Mini) over the air, but it keeps telling me that I'm already up to date. I also get the same result on iTunes. I've also gone the route of downloading the official iOS 7 IPSW and doing option-check for updates or option-restore on my Mac, but every one I've tried it, iTunes tells me that I'm using an incorrect firmware. Could someone help me out here?

Even though its "beta 6" it is the version everyone else is getting

To get it early you have to go to the apple development program that costs $99 yearly and there will be instruction from there

Simplest way:
1.updated to iTunes 11.1
2. Plug your iPhone, iPad, or iPod touch into iTunes
3. Let iTunes download and re-install iOS 7

Or you could download ipsw & shift update from iTunes.links to IPSW files are available at http://osxdaily.com/2013/09/18/ios-7-ipsw-direct-download-links/