Are there only three screens to display apps on the ipad? I just downloaded an app that filled up my third screen and it put it right over another one

hold,just drag to the right. not sure how many screen, i have a search screen and a fourth screen with 5 apps on. you can always drag again and see, i just have not bothered to go any further.

You get 11 screens not including the search screen.
They only show the screens that have apps. So if you have 3 screens with apps you will only see three screens. You can move icons onto a new screen by dragging them to the far righ of the screen until it pulls up a new page.