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Sums of Geometric Sequences : Checkerboard Problem

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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 checker board 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 expressed in dollars would Mr. Brown have to put on the 32nd square?
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?

https://brainmass.com/math/algebra/sums-of-geometric-sequences-checkerboard-problem-121114

Solution Preview

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 ...

Solution Summary

The sum of a geometric sequence is investigated.

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