Rotationally resolved transitions from the metastable 4s sigma a(3) Sigma(u)(+) state of Ar-2 to the 7 p sigma (3) Sigma(g)(+) state have been observed by laser excitation spectroscopy in a pulsed corona discharge. Laser induced fluorescence spectra for the 7 p sigma (3) Sigma(g)(+) <-- a (3) Sigma(u)(+) transition observed near 19 530 cm(-1) have led to the first resolved triplet splittings and rotational analyses for Rydberg-Rydberg transitions in Ar-2. Analyses for the (0-0), (0-1), (1-0), and (1-1) bands of 7 p sigma <-- a are presented here. Bands with v’=2 are observed for this system but exhibit no rotational structure and bands with v’>2 are not observed, indicating that the predissociation lifetimes of these upper levels fall rapidly for v’>1. Data presented lead to rotational energies and molecular constants for the a(3) Sigma(u)(+) and 7 p sigma (3) Sigma(g)(+) states, including the effective rotational constant B-e which is determined to be 0.1412 cm(-1) and 0.1345 cm(-1) for the 4s sigma a(3) Sigma(u)(+) and 7p sigma (3) Sigma(g)(+) states, respectively. Results are compared to ab initio and other calculations, and combined with existing data to produce experimental estimates of D-0 and D-e for the a (3) Sigma(u)(+) state of 5700+/-200 cm(-1) and 5850+/-200 cm(-1), respectively.