It's too late to backup now. You have to restore your iPad. You will lose everything on the device. Having an iTunes account has nothing at all to do with any of this. Besides, I think that you mean that have ever synced with iTunes. And once again, it doesn't matter. You still have to restore the device using iTunes.
There is no other option - that is if you want to use your iPad again, there is no other option.
Read this for more information and for the instructions. There are several ways to restore your iPad, you can use any computer that is running iTunes, if you do not have a computer of your own.
You will be able to download most of your paid content again as well, if you have no backup and I think we have established that you do not have one.Take a look at this.
If you can’t update or restore your iOS device
iPad Stuck in Recovery Mode after Update
In order to get your iPhone out of recovery mode, you can have a try of iPhone Data Recovery software, which helps iDevice users to restore and save their iPhone data, besides, in your situation, it also works. It supports to fix iPhone stuck in recovery mode issues, you can just download the trial version and have a try!
I was getting a software update when my screen turned black and then showed the iTunes icon with a USB/charger thing with arrow pointing to the iTunes icon. My iPad will not respond to any other commands. I did some research and based on what I found I think I am stuck in recovery mode. Is there a possible way to get out of recovery mode and not lose all of my iPads data? Also I do not have an iTunes account. I would be extremely disappointed if my iPad lost all of its data. Thank you and if you see this and know how to get out of recovery mode PLEASE help I am desperate. THX
I fix it by using iTuens, here we go:
Press down the Home and Power buttons on your iPad until it shuts off.
Connect iPad to your computer with the USB cable.
Press and hold down the Home button.
Hold it down until iTunes says your device is entering recovery mode.
Now you should be able to Restore using iTunes.
If it can't work out your problem, you can use iPhone Data Recovery to kick your iPad out of recovery mode.