When I purchase music on iTunes on my PC, it gives me the option to download it on my iPad but not the other way round. There must be a way of doing it but I can't find it. I'm pretty sure I have the latest version of iTunes.
Welcome to the Support Communities!
There are actually three ways to do this. One is to change your preferences in your iTunes application on your computer to Automatically download anything you purchase. See the link below for instructions:
You can also download anything you've purchased from the iTunes Store to your computer at any time:
And finally, you can transfer purchases from your iPad to your computer when you backup your iPad.
Hope this helps ...