It has been a *while* since I've had my grubby little hands in an Apple iThingy of any sort; but I recall having to do excatly this a few times with my kids' older iPads. In the App Store - **if I recall correctly** (**IF**) - I had to somehow navigate to "My Purchases" (or somethng to that effect). That page listed all of the apps I'd ever downloaded. From that page I could select an app that I knew was too new for the iPad I was using; but sure enough, I was prompted to download the last version of the app that will work on this device.
With that said, some older versions of apps may use echnologies that the developers have discontinued.
EDIT:
@PimTac , I have just realized, posted this exact information a couple of posts above mine; but much better.