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Question 44372: I'm having problem soving the following problems. Please help.
2) Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
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b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
Answer:
Show work in this space.
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer:
Show work in this space
3) Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.
Answer:
Show work in this space.
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.
Answer:
Show work in this space.
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
4) CLASSIC PROBLEM - 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 expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! 2) Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
r = 2
Show work in this space.
2/1=4/2=8/4=2 IS THE COMMON RATIO WHICH IS CONSTANT
b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
Answer:
a24 = 8388608
Show work in this space.
TN=A*R^(N-1)...WHERE
TN=N TH. TERM
A= FIRST TERM
N= NUMBER OF TERMS
T24=1*2^(24-1)=2^23 =8388608
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer:
Sum a10 = 1023
Show work in this space
SN=A*(R^N -1)/(R-1)
= 1*(2^10 -1)/(2-1)=1023
3) Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
r = 1/2
OK
Show work in this space.
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.
Answer:
S10...N=10 SUM IS BETTER SHOWN BY S...A IS FOR TERM
Show work in this space.
SN=1*{1-0.5^N}/(1-0.5)
S10= 1..99805
OK
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.
Answer:
s10 = 1.9995
OK
ANSWER IS 1*{1-0.5^12-1}/(1-0.5)
=1.9995
- Show quoted text -
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
The Sum is always smaller than 2.
N
a
Sum
0
1
1
1
0.5
1.5
2
0.25
1.75
3
0.125
1.875
4
0.0625
1.9375
5
0.03125
1.96875
6
0.015625
1.984375
7
0.007813
1.992188
8
0.003906
1.996094
9
0.001953
1.998047
10
0.000977
1.999023
11
0.000488
1.999512
12
0.000244
1.999756
4) CLASSIC PROBLEM - 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 expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
$ 21474836.48
Show work in this space
an = .01*2n-1
a32 = .01*232-1
a32 = .01*231
a32 = .01 * 2147483648
a32 = 21474836.48
OK
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
$42949673.00
Show work in this space
Sum an = .01 * (2n - 1) / ( 2 - 1 )
Sum a32 = .01 * (232 - 1) / ( 2 - 1 )
Sum a32 = 42949673.00
OK
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?
Answer:
$184467000000000000.00
Show work in this space
Sum an = .01 * (2n - 1) / ( 2 - 1 )
Sum a64 = .01 * (264 - 1) / ( 2 - 1 )
Sum a64 = 184467000000000000.00..
OK
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