We present the first results from the largest spectroscopic survey to date of an intermediate redshift galaxy cluster , the z = 0.834 cluster RX J0152.7-1357 . We use the colors of galaxies , assembled from a D \sim 12 Mpc region centered on the cluster , to investigate the properties of the red-sequence as a function of density and clustercentric radius . Our wide-field multi-slit survey with a low-dispersion prism ( LDP ) in the IMACS spectrograph at the 6.5 m Baade telescope allowed us to identify 475 new members of the cluster and its surrounding large-scale structure with a redshift accuracy of \sigma _ { z } / ( 1 + z ) \approx 1 \% and a contamination rate of \sim 2 \% for galaxies with i ^ { \prime } < 23.75 mag . We combine these new members with the 279 previously known spectroscopic members to give a total of 754 galaxies from which we obtain a mass-limited sample of 300 galaxies with stellar masses M > 4 \times 10 ^ { 10 } M _ { \odot } ( \log M / M _ { \odot } > ~ { } 10.6 ) . We find that the red galaxy fraction is 93 \pm 3 \% in the two merging cores of the cluster and declines to a level of 64 \pm 3 \% at projected clustercentric radii R \gtrsim 3 Mpc . At these large projected distances , the correlation between clustercentric radius and local density is nonexistent . This allows an assessment of the influence of the local environment on galaxy evolution , as opposed to mechanisms that operate on cluster scales ( e.g . harassment , ram-pressure stripping ) . Even beyond R > 3 Mpc we find an increasing fraction of red galaxies with increasing local density . The red galaxy fraction at the highest local densities in two large groups at R > 3 Mpc matches the red galaxy fraction found in the two cores . Strikingly , galaxies at intermediate densities at R > 3 Mpc , that are not obvious members of groups , also show signs of an enhanced red galaxy fraction . Our results point to such intermediate density regions and the groups in the outskirts of the cluster , as sites where the local environment influences the transition of galaxies onto the red-sequence .