AN A320 CREW ON APCH INTO SEA RECEIVE A TCASII TA THEN AN RA WHILE ON A 3 MI FINAL AT APPROX 1000-1200 FT. CREW STOPPED A C172 XING BELOW THEIR ACFT.

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ON APCH TO RWY 16R WITH SEA TWR; AT 3 MI FINAL; GOT A TA AT APPROX 10 O'CLOCK POS. FO CALLED OUT TFC IN SIGHT LOW AT 10 O'CLOCK POS (A C172). A SHORT TIME LATER WE RECEIVED AN RA 'MONITOR VERT SPD' WHICH THE PF COMPLIED WITH. RA LASTED ABOUT 2-3 SECONDS UPON WHICH WE RECEIVED A CLR OF CONFLICT CALL ON TCASII. FO ESTIMATED TFC CROSSED UNDERNEATH US APPROX 700 FT. ATC DID NOT CALL THE TFC AT ANY TIME NOR DID IT APPEAR THAT THE CESSNA WAS IN CONTACT WITH ATC WHEN THEY WERE INSIDE THE TCA BY MY ESTIMATION. TOLD TWR AND THEY SAID THAT THEY WOULD MENTION IT TO THE SUPVR. SUPPLEMENTAL INFO FROM ACN 636693: ON FINAL TO RWY 16R SEA AT APPROX 1000-1200 FT AGL; CTRED ON ILS GS; TCASII TA 'TFC' RECEIVED. YELLOW TCASII TFC TARGET APPEARED AT 11:30 O'CLOCK POS WITH ALT DISPLAYED AS -800 FT. I LOOKED TOWARD DIRECTION OF CONFLICT AND SAW A WHITE C150/C172 WITH BROWN OR DARK STRIPING BELOW OUR ACFT AND PERHAPS LESS THAN 2500 FT. THE ACFT WAS CLOSING TOWARD US. IMMEDIATELY WE RECEIVED A TCASII RA 'MONITOR VERT SPD.' THE PF COMPLIED WITH THE RA. THE ACFT APPARENTLY PASSED DIRECTLY UNDERNEATH US. WHEN CLR OF CONFLICT MESSAGE RECEIVED; WE WERE AT APPROX 600 FT. TWR NOTIFIED OF EVENT. FEMALE TWR CTLR SAID THAT SHE WOULD ADVISE HER SUPVR. AFTER EXITING RWY; ADVISED SEA GND CTL TO TELL TWR THAT WE RECEIVED AN RA; JUST TO CLARIFY SIT. C150/C172 CERTAINLY ENCROACHED RWY 16L AND 16R FINALS. TWR NEVER ADVISED US OF THE TFC. I CAN'T THINK OF ANY REASON FOR THAT ACFT TO BE AT 500 FT AGL OR SO UNDER THE FLT PATHS OF A CAT X ARPT.