Driving Process

Tom and Mary will travel to Los Angeles during their Charismas holiday. They plan to start their trip from Oklahoma City and drive half of the distance from Oklahoma City to Los Angeles on their first day, then drive half of the remaining distance every day until they get to Los Angeles.

What is known:

• The total distance is 1400 miles
• Each day they drive 1/2 of the remaining distance
• It is assumed that they get Los Angeles when the remain distance is less than 10 miles.

When will they get within 10 miles of Los Angeles finially?

• The driving process forms a sequence:
  a_n = 1/2, 1/4,1/8, ..., 1/2ⁿ, ...