American Airlines (AA) flight 2905 encountered turbulence at flight level (FL) 250 [25,000 ft] while enroute to Charlotte Douglas International Airport (CLT) Charlotte, North Carolina. One flight attendant was seriously injured, and 3 flight attendants sustained minor injuries as a result of the turbulence. The flight was a regularly scheduled domestic passenger flight from Tampa International Airport (TPA), Tampa, Florida to CLT. After reviewing the weather prior to flight, the flight crew stated they opted for a cruising altitude of FL250 based on a PIREP [pilot report] describing smooth air between FL250 and FL260. During cruise, they did not observe weather in the 100 miles ahead of them and the clouds they saw appeared to be below them. As they approached top of descent, the crew described going “heads down” for a few minutes to load performance data into the flight management computer and to review the arrival procedure into Charlotte. The crew described that when they looked up, they saw a rapidly building cumulous cloud directly ahead of the airplane, too close to maneuver around. The first officer immediately illuminated the seat belt sign and the airplane penetrated the top of the cloud. Flight data showed that during the event, the airplane encountered load factors ranging from about 0.17g to 2.75g, which classifies as extreme turbulence. The flight attendants had just completed beverage service and were collecting trash at the time the aircraft encountered the turbulence. Flight attendant 3 and 4 were standing by the aft left door preparing the trash cart, flight attendant 2 was on the opposite side of the cart which was lined up to go down the aisle. During the turbulence the trash cart fell on to flight attendants 3 and 4, and flight attendant 2 fell onto the trash cart. Flight attendant 3 fractured both ankles, and flight attendants 2 and 4 suffered minor injuries. These three flight attendants were unable to complete their duties and were secured in passenger seats for the reminder of the flight. The flight crew declared an emergency and continued the flight into CLT. An off-duty pilot and off-duty flight attendant assisted flight attendant 1 with securing the cabin and manned the aft jumpseats for landing. The landing was uneventful. Paramedics met the aircraft at the gate and transported the injured flight attendants to the hospital.