After connecting using HDMI, go to Windows Display properties and check if you see two display devices- one should be your default monitor and the other should be Digital Display Device (this will be your TV). If you see your TV listed, try manually switching your display to TV to check if your TV then receives the signal.
Typically, if your Graphics card is able to detect the connected HDMI display device (your TV in this case), it will retrieve all supported resolutions of your TV and then automatically select the optimum resolution.