A B727 FLC USES TCASII TO AVOID A DSNDING SKYDIVER ACFT NW OF PVD; RI. TA NOT GIVEN.

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ON DEP FROM PVD; PVD RADAR CTL ASSIGNED A NW HDG FOR AN ACFT DROPPING SKYDIVERS. WE WERE CLBING TO OUR ASSIGNED ALT OF 10000 FT OR 12000 FT. ON THE ASSIGNED HDG; WE RECEIVED A TA WARNING ON TCASII. CREW STARTED LOOKING FOR TFC. I INSTRUCTED PF TO START LEVELING OFF. ACFT ON TCASII WAS ABOVE US AND DSNDING. BEFORE WE COULD ACQUIRE A VISUAL ON ACFT; OUR TCASII TURNED INTO AN RA. WE FOLLOWED OUR TCASII DIRECTION FOR RA. TCASII COMMANDED A DSCNT OF ABOUT 1500 FT DOWN. WE STARTED OUR DSCNT AT 8500 FT AND TCASII STATED 'CLR OF CONFLICT' AT ABOUT 7500 FT. ABOUT THIS SAME TIME WE HAD A VISUAL ON THE TFC (A HIGH WING; SINGLE ENG CESSNA) AND STARTED TO LEVEL OFF. THE COPLT WAS THE PF. WHILE HE WAS DSNDING; I INFORMED ATC THAT 'WE HAVE A TCASII RA AND WE ARE DSNDING.' HE ACKNOWLEDGED OUR XMISSION. AFTER THE CONFLICT WAS OVER AND WE WERE CLBING BACK TO ASSIGNED ALT; I INQUIRED TO ATC WHETHER OR NOT HE HAD THAT ACFT OR RADAR; AND HIS RESPONSE WAS; 'I HAVE SEVERAL ACFT OUT THERE; SOME WITH MODE C AND SOME WITHOUT.' I FEEL THAT MY CREW DID AN EXCELLENT JOB FOLLOWING COMPANY PROCS AND SOP PER OUR TCASII TRAINING. IF ATC WOULD HAVE ADVISED US OF VFR TFC WITH MODE C; WE WOULD HAVE HAD MORE OPTIONS SOONER.