A LOW TIME CFI MADE AN EMER LNDG AT MSN AFTER THE THROTTLE SEIZED ON HIS C172RG.

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WE (MYSELF AND A PVT STUDENT) WERE ON FINAL APCH TO RWY 32 INTO MADISON; WI; TRAUX FIELD. MY STUDENT WAS LOW AND I ASKED HIM TO ADD MORE PWR. THERE WAS NO TO CLB. I TOLD HIM TO PITCH FOR BEST GLIDE AND CONTINUE TOWARDS THE RWY WHILE I TROUBLESHOT THE STUCK THROTTLE. I INITIALLY THOUGHT CARB ICE; BUT VERIFIED THAT THE CARB HEAT WAS ACTIVATED. I THEN CHKED THE FUEL SELECTOR VALVE (ON); MIXTURE (FULL RICH); PROP (FULL FORWARD); THROTTLE (FULL FORWARD); IGNITION (ON); PRIMER (IN AND LOCKED); AND MASTER (ON). UPON REACHING THE RWY (WE HAD EXCESS ALT); TOLD HIM TO CUT THE THROTTLE TO IDLE AND ADD FULL FLAPS TO GET US DOWN. HE DROPPED FULL FLAPS AND RETARDED THE THROTTLE. HOWEVER; HE STILL HAD ABOUT 1700 RPM BEING PRODUCED. I TOOK THE CTLS AND TRIED TO EXECUTE A GAR -- NOT ENOUGH PWR TO PRODUCE LIFT! I THEN MADE THE PIC DECISION TO CUT THE ENG AND LAND THE ACFT. WE WERE NOT ABLE TO CLB OR DSND DUE TO OUR THROTTLE BEING STUCK AT 1700 RPM. I LANDED THE ACFT SAFELY ON THE RWY (320 DEGS) AND ADVISED TWR OF OUR SIT. WE LATER FOUND THAT THE BOLT AND NUT THAT HOLDS THE THROTTLE ROD END TO THE THROTTLE ARM WAS MISSING -- NON EXISTENT! THUS; WE HAD NO CTL OF OUR THRUST. I BELIEVE THAT THE MECHS DID NOT PLACE A COTTER PIN TO LOCK THE NUT IN PLACE. THE DAY PRIOR TO THIS EVENT; A NEW PROP CABLE WAS INSTALLED; AND I THINK THIS WAS ALL DUE TO HUMAN ERROR. THE ONLY THING THAT I SHOULD HAVE DONE DIFFERENTLY WAS DECLARED AN EMER IN CASE I WAS NOT ABLE TO PLACE THE ACFT SAFELY ON THE RWY. IN THE HEAT OF TAKING ACTIONS TO SAFELY GET THE ACFT DOWN; I FORGOT TO DECLARE AN EMER. I FEEL THAT THE MAINT PROGRAM AT MY FLT SCHOOL NEEDS TO BE DRASTICALLY IMPROVED; SO THAT INSTANCES LIKE THIS DO NOT OCCUR.