Yes, your spoon is silverplated. Rogers & Bro. is the name of the manufaccturer, which was located in Waterbury CT. There were several "Rogers" brothers outfits in silver manufacturing in the late 1800's, including C. Rogers & Bros., who was sued by Rogers & Bro. for using their name, but were unable to stop the usage. Tthey were later bought by International Silver Co. in the early 20th century, but continued to use their mark.
The A1 mark was used to denote silver plate.
http://www.925-1000.com/silverplate_R.html