One shared resistor is only OK when the software is written to drive one segment at a time. But to get the correct intensity, the current through the segment must then be adapted for the 7:1 (or possible 8:1) multiplexing ratio. Not all LED can support the high currents needed to display multiplexed data with maintained intensity. And a failing program that stops multiplexing could send seven times the highest static current through a single segment and kill the display.

So unless you have very specific reasons for displaying the segments one at a time, you should follow Andys recommendation and have one resistor for each segment instead of having it on a common anode or cathode.