A B-737 FLT CREW MISUNDERSTANDS TAXI INSTRUCTIONS AND TAXIED ON WRONG TXWY.

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DETROIT INTERNATIONAL. CLRED TO TAXI FROM THE GATE TO RWY 21R VIA TXWY MIKE. DURING TAXI ON TXWY MIKE; WE WERE RUNNING THE PRETKOF CHKLIST AND TAXIED BEYOND THE LAST INTXN FOR THE TKOF END OF RWY 21R. WE CONTINUED TO TAXI ON THE TXWY MIKE UP TO THE FIRST INTXN ON THE L. WE CONTACTED GND CTL AND ADVISED THEM THAT WE HAD MISSED THE LAST INTXN FOR RWY 21R. GND CTL ASKED US IF WE COULD MAKE THE L TURN AT THE INTXN THAT WAS DIRECTLY IN FRONT OF US. WE ANSWERED AFFIRMATIVE AND CONTINUED OUR TAXI ON THE UNNAMED TXWY; REVERSED OUR DIRECTION ONTO THE DE-ICE PAD AND CONTINUED TO THE END OF RWY 21R. (ATC DID NOT EXPRESS ANY CONTENTION WITH OUR ACTIONS.) WE DEPARTED WITHOUT INCIDENT. I BELIEVE WE MISSED THE LAST INTXN BECAUSE 1) TXWY MIKE CONTINUES BEYOND THE TKOF END OF RWY 21R AT LEAST 2000 FT OR SO; AND DOES NOT CHANGE IN WIDTH OR SURFACE MATERIAL. IT GIVES THE APPEARANCE THAT YOU MUST TAXI FURTHER TO GET TO THE END OF THE RWY. 2) THE SIGNAGE PLACEMENT FOR THE PRECEDING AND END INTXN SEEMS NON-STANDARD. WHEN WE REVERSED COURSE; THE FIRST PART OF THE INTXN WAS PROPERLY MARKED (PAINTED WITH HOLD LINES). AS WE BEGAN THE SECOND 90 DEG TURN; THE TXWY WAS NOT CLEARLY MARKED (NO WT LIMITATIONS WERE NOTED ON CHART). THIS SITUATION COULD BE AVOIDED BY: (1) PAYING CLOSER ATTN DURING TAXI (CREW); (2) BETTER PLACEMENT OF TXWY SIGNS DESIGNATING THE END OF THE (RWY 21R).