I configured the IP address and telnet for my Cisco router but on GNS3 it shows a different IP address. When I ping the router from my Ubuntu virtual machine using the IP address I configured the ping fails. However, when I ping the router using the IP address shown on GNS3 the ping is successful. I am not sure very familiar with GNS3 as we just started it in college and would appreciate help.
You have to distinguish between the simulated network and the control of the simulator. The router is part of the simulation -- its networks are also part of the simulation.
In real life, the console port of the router is a serial connection. It doesn't have an IP address. The console is used to initially configure the device (among other things). The GNS3 simulator lets you access console port via an IP address.
You can connect your PC to the simulated network by explicitly configuring that in GNS3.