Installing Python 3.10

Firstly, update your repository listings and system packages.

$ sudo apt update && sudo apt upgrade -y

Once that is done we can proceed to install the required dependencies.

$ sudo apt install software-properties-common -y

Then add the deadsnakes PPA to the APT Sources List.

$ sudo add-apt-repository ppa:deadsnakes/ppa

You will see the following output:

To install 3rd-party Python modules, you should use the common Python packaging tools.  
For an introduction into the Python packaging ecosystem and its tools, refer to the Python Packaging User Guide:

The package sources are available at:

Nightly Builds

For nightly builds, see ppa:deadsnakes/nightly
More info:
Press [ENTER] to continue or ctrl-c to cancel adding it

After this we can install Python 3.10.

sudo apt install python3.10