Consider this dialogue from a 2006 Foxtrot cartoon by Bill Amend:
Paige is sitting at a desk and reading from a paper, while her brother Peter listens...
Paige: "A math teacher offers to assign one second of homework the first week of school. two seconds the second week, four seconds the third, and so on."
Paige: "If the amount of homework doubles every week, is this something you would agree to for the duration of the 36-week school year?
Paige: "I'm a little worried about answering this one wrong."
Peter: "Is that Mr. Thompson? He's evil."
Your Question #1: What is the length of the homework assignment in the 36th week?
Your Question #2: What is the average length of a homework assignment per week over the 36-weeks?
Hint: Write down the homework time for first five weeks...look for patterns.
Solution Commentary: For a similar problem, consider the Wheat and Chessboard Dilemma.