SOLUTION: 4) A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady o

Question 26309: 4) A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter�s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, �If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.� As he�d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money would Mr. Brown have to put on the 32nd square?

Found 2 solutions by stanbon, Earlsdon:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The squares have 1, then 2, then 4, then 8 .....then 2^63 pennies.
The 32nd square will have 2^31 pennies.
2^31=$21,474,836.48 on it.
Cheers,
Stan H.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
This is a variation an old story.
By placing 1 penny on the first square, two pennies on the second square, three pennies on the third square, etc, Farmer Brown is creating a geometric sequence in which each term can be represented by: (an) where n = the ordinal number of the term. So, a(1) is the first term, a(2) is the second term, etc.
The nth term of such a sequence is given by: where a(1) is the first term and (r) is the common ratio and is found by.
In this problem, r = 2 and a(1) = 1 (penny)
The 32nd term would be = and, since this is the number of pennies, this would amount to $21,474,836.48
Note: a(1) means... a sub 1
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