geometric series

goldcantstay

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Nov 30, 2006
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"In 1935 the famous "Prosperity Club" chain letter caused quite a stir throughout the US. The letter contained a list of 6 names and addresses and asked you to send a dime to the person at the top of the list and remove his or her name. You were then to add your name to the bottom of the list and pass the letter on to 5 friends. These 5 friends made up the second level in the chain.

a) Write several terms of the sequence of the # of people at each level of the chain:
ok, easy. 1, 5, 25, 125, 625 etc, x 5

B is what I can't figure out

b) The letter claimed that if you did not break the chain, you would receive a certain amount of money. How much?

c) The population of the US in 1935 was about 127,250,000. Assuming no duplications, how many levels would it take for the entire population of the United States to receive the chain letter.
Thirteen levels for C
 
What's easy about the first part?

Problem Statement

"The letter contained a list of 6 names"

Your Sequence

"1, 5, 25, 125, 625"

How do the first two terms fit into the problem statement?
 
goldcantstay said:
"In 1935 the famous "Prosperity Club" chain letter caused quite a stir throughout the US. The letter contained a list of 6 names and addresses and asked you to send a dime to the person at the top of the list and remove his or her name. You were then to add your name to the bottom of the list and pass the letter on to 5 friends. These 5 friends made up the second level in the chain.

a) Write several terms of the sequence of the # of people at each level of the chain:
ok, easy. 1, 5, 25, 125, 625 etc, x 5

B is what I can't figure out

b) The letter claimed that if you did not break the chain, you would receive a certain amount of money. How much?

c) The population of the US in 1935 was about 127,250,000. Assuming no duplications, how many levels would it take for the entire population of the United States to receive the chain letter.
Thirteen levels for C

First person receives .10 cent.
Your name is now at the bottom of the list.
Your name will be at the top of the list after 5 mailings..
You send it to 5 people who send .10 cents to the top name = .50 cents in total.
Your name is now 5th from the top.
Each of these 5 people send it to 5 more people, for 25 in total.
Each of the 25 sends .10 cents to the top name for $2.50 in total.
Your name is now 4th from the top.
Each of these 25 people send it too 5 more people, or 125 in total.
Each of these 125 send .10 cents to 125 people for $12.50 in total.
Your name is now 3rd from the top.
Each of these 125 people sent it to 5 more people, or 625 in total.
Each of these people send .10 cent to 625 people for $62.50 in total.
Your name is now 3rd from the top.
Each of these 625 people sent it to 5 more people, or 3125 inn total.
Each of these 3125 people send .10 cents to 3125 people ffor $312.50 in total.
Your name is now 2nd on the list.
Each of these 3125 people send it to 3125 people, or 15,625 in total.
Each of these 15,625 people send .10 cents to 15,625 people for $1,562.50 in total.
Your name is now number one on the list.
Each of these 15,625 perple send the letter to 5 more people, or 78,125 in total.
Your name is at the top of the list.
Therefore, each of 78,125 people send you .10 cent for a grand total of $7812.50.

a)1-5-25-625-3125-15,625-78,125 would be the sequence of people involved.

b) Inn the end, you receive $7812.50

c) 5^10 = 9,765,625
5^11 = 48,828,125
5^12 = 244,140,625
Therefore, it would take 12 mailings to reach the stated population.


I hope I didn't slip a number. If I did, please let me know.
 
tkhunny said:
You didn't answer my objection.

The person who started the letter is 1.

Those that he sent the letter to makes 5.

Each of these 5 send to 5 more making the next total 25.

I thuik the rest follows naturally.

What are you reading into or out of the problem statement that leads you to consider the sequence to be incorrect?
 
I agree that it follows, but how does it start. The first letter needs six names.
 
tkhunny said:
I agree that it follows, but how does it start. The first letter needs six names.

The first person who, wrote and started the letter, created a list of 6 names, his being at the bottom.

He sends a dime to the name on the top of the list.

He is therefore the first person involved in the sequence..

Those that he sends the letter to makes 5 more people receiving the letter., not 6, with his name at the bottom of the letter in the 6th position..

Each of these 5 send to 5 more making the next total 25.

The rest follows naturally, 25-625-3125-15,625-78,125.

At no time is there 6 people receiving or sending letters.
 
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