Adam proposes that his mother changes his allowance according to the
following rule: “The first week, you'll only give me $.02. Then each week
after the first week, you'll pay twice what you paid the week before." He
explains that even though this is less than the $5 per week he gets now,
he will feel better because he will always get more than he got the
previous week.
a. If Adam's mother agrees with him, how much will Adam receive in the
fifth week?
b. How much will his allowance be in the tenth week? In the fifteenth week?