I downloaded Bitcoin core to my computer and after that I bought some bitcoins. I didn't realized that my bitcoin core was not synced, after 3 days waiting to finish now my deposit is not showing in my wallet. What can I do?
Depends on which wallet you 'bought' the coins. If it was a paper wallet/ mobile app wallet/ some other wallet software, then obviously it won't come up in the Bitcoin core wallet software. Just FYI, Bitcoin core comes coupled with a lot of other utilities apart from making you machine act as a full node. It has a built in wallet whose balance and other details are accessible via the command line interface, bitcoin-cli or the GUI bitcoin-qt.
Assuming you did not use the Bitcoin core wallet, you need to first import the private and public keys to get the balance. You can go through the API documentation of the bitcoin core. The following links might be useful