Question 33579: I need help!!! Please!!
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 greatefully thanked the traveling salesman for saving his daughter's life. Mr. Brown insisted on giving the man a reward 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 a reward, 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?
b). How much would the traveling salesman receive if the checkerboard only had
32 squares?
c). Calculate the amount of money necessary to fill the whole checkboard (64 squares). How much money would the farmer need to give the salesman?
Any and all help you can give on this problem, would surely be appreciated!! Thanks in advance!
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! This is an example of a "geometric sequence" in which the common ratio, r = 2
1, 2, 4, 8, 16, 32, 64, ...  where n = the number of the square.
So, for the 32nd square, Mr Brown would have to put  pennies.
This would amount to  pennies.
Divide this by 100 to get the number of dollars.
a) $21,474,836.48
b) To find the sum of the pennies on 32 squares, you need to find the partial sum of the of the first 32 terms of the geometric sequence, called a geometric series. The partial sum of the first n terms of a geometric series is given by where: a1 is the first term (1), r is the common ratio (2) and, for 32 terms (squares), n = 32.
So, with a1 = 1 and r = 2, this simplifies to
If the checker board had only 32 squares, it would require pennies to fill the board. This would amount to:
$42,949,672.95
To fill the entire board of 64 squares would take pennies.
 pennies. This would amount to:
$184,467,440,737,095,516.15
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