I've downloaded Tumblr on to my iPad 2 and the button in the App Store now shows OPEN.
But when I tap the 'OPEN' button, nothing appears (it's just the same!)
I checked it again after resetting the home screen view so it's arranged. I searched for 'T' and there's no Tumblr!
Maybe it's bit blurry, but there's all the apps which started with T. I've searched in the search Spotlight too but also, nothing appears with 'Tumblr'.
Best Answer
Reboot the device by holding both the power and home button until the Apple logo is shown. This will reset the SpringBoard cache which should show the app on the home screen if it's been downloaded (and in Spotlight).