As the cost of mapping a person’s genome falls, some experts and health-care companies are predicting that genome sequencing will one day become common practice in doctors’ offices and hospitals as a means of guiding prevention and treatment of illnesses. Robert C. Green, HMS lecturer on medicine at Brigham and Women’s Hospital, is leading a trial to see what patients and their primary-care doctors do with the genetic information, including changing lifestyle, prescribing drugs and ordering additional tests.