Facebook no longer works in settings but the app does
A couple of months ago, I changed the password for my Facebook account and when I looked on my iPad in Settings and then the Facebook part of the Settings, it now says "There was a problem accessing your account. Please re-enter the password for My Name:. It then has the Password field with required in grey. When I go and put my password in and press either Done at the top of the corner or Return on the keyboard, it keeps on bringing the message up with Error Signing In as the title and then The username or password is incorrect. My password isn't incorrect when I am putting it in. The strange thing though is that the app works perfectly fine.
I am completely stuck for a solution, I've tried resetting my iPad to see if it works and it hasn't. I've also removed the app and then re-install the app from the settings and signing in like I would normally do on my iPad.
This now also means that when I get apps that might require a Facebook connection, it won't connect because obviously according to the iPad, there is no Facebook account linked/the Facebook account isn't signed in.
Specifications
iPad 2 - 16GB
iOS 7.1.1
Printscreens