Back to basics. Def: Common Cathode
Vf (forward voltage drop) It's different for different colors. At 24V we can probably neglect. In the range of 1.2 to 3.2 Volts.
If (Forward current) In the range of 1 to 50 mA for displays and probably single LED's too.
It's best to put a series resistor for EACH segment. Rs = (V-Vf-Vother)/If. Vother can be Vce(sat) for instance.
Common Cathode means that that the segments common connection is the (-) of the supply. Assuming the supply has (+) and (-) terminals.
If you can get a single LED to light, your half way there. The cathode of a satandard T 1 3/4 LED is the side with the flat. Put a resistor to +24, the LED, the Flat portion to (-) and the LED should light.
Now extrapolate that to the display case.