iPhone Apps
Downloaded App not showing on Home Screen.
Windows, Windows 6
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go to Settings > General > About.. what is your Software Version?
If you are running iOS 14, downloaded apps may be going to the App Library
From your Home Screen, swipe left until you get to the App Library.
Swipe downward and you'll get an alphabetical list of your apps.
Locate the app in the list or type the app name into the search field
Once you've located the app, tap/hold until it raises/selects, then drag it and it'll pop out to your Home Screen
Organize the Home Screen and App Library on your iPhone - Apple Support
If you want your downloaded apps to go to the Home Screen as well,
go to Settings > Home Screen and check 'Add to Home Screen'