Chapter 6.2, Problem 73E

Chain letters Suppose you receive a chain letter with six names on it, and to keep the chain unbroken, you are to mail a dime to the person whose name is at the top, cross out the top name, add your name to the bottom, and mail it to five friends. If your friends mail out five letters each and no one breaks the chain, you will eventually receive dimes. How many sets of mailings must occur before your name is at the top of the list to receive dimes? How many dimes would you receive? (This is a geometric sequence with first term 5.)