How to check if a package is installed on Linux

On RPM based system

on RPM based systems like Red Hat, Cent OS etc, we can use rpm query command like below :

rpm -qa | grep telnet

or 

rpm -q telnet

If system is configured with YUM then it can list all installed packages for you and you can grep out your desired package from it.

yum list installed | grep telnet

On APT based systems 
on APT based systems like Debian, Ubuntu etc, dpkg command can be used to verify if package is installed

dpkg -l | grep telnet