Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 37824: Determine which of the following can be the first three terms of an Arithmetic sequence.
a. 1/2,1/4,1/8
b. -8,-16,-32
c. -42,-37,-32
d. 4,-1,6
I have no idea which one it is. Could you please help me? Thank you.
Click here to see answer by fractalier(6550)   |
Question 37792: A tank contains gallons of water. Each day one-third of the water in the tank is removed and not replaced. How much water remains in the tank at the end of 6 days?
i tried doing this a few times and im not getting the right answer. I think you write it like this: a=5832(1/3)^(6-1) right?
Click here to see answer by fractalier(6550) |
Question 38033: The executive committee of the student government consists of 10 members. In how many ways can a chair, vice-chair, secretary, and a treasure be chosen, assuming one person cannot hold more than one position? Please help!
Click here to see answer by stanbon(75887) |
Question 38571: Compare the values in Column A and Column B for the solution of the system:
{ x + y + z = 10
x + y + 2z = 13
x + y + 3z = 16
Column A = x
Column B = y
A The value in Column A is greater
B The value in Column B is greater
C The two values are equal
D The relationship cannot be determined on the basis of the information supplied
I'm just not sure!!! Thanks!!
Click here to see answer by AnlytcPhil(1806)  |
Question 38761: 3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… 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? Carry all calculations to 7 significant figures.
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? Carry all calculations to 7 significant figures.
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:
Click here to see answer by Nate(3500) |
Question 39011: Don't know how to do these. Please help.
3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… 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? Carry all calculations to 7 significant figures.
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? Carry all calculations to 7 significant figures.
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:
Click here to see answer by stanbon(75887) |
Question 39196: This is my last question, Thanks for all your help everybody.
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 Crane came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Crane 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 grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat.” As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
a) How much wheat would Mr. Brown have to put on the 24nd square?
Answer:
Show work in this space.
b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Answer:
Show work in this space.
c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
Answer:
Click here to see answer by stanbon(75887) |
Question 39195: Still do not understand. Please help again.
3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… 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? Carry all calculations to 7 significant figures.
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? Carry all calculations to 7 significant figures.
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:
Click here to see answer by stanbon(75887) |
Question 39191: Still need help. PLease if anyone can help, it would be very appreciated. Thank you.
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a) What is d, the difference between any 2 terms?
Answer:
Show work in this space.
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space.
Click here to see answer by kathysmiles77777(4) |
Question 39190: Still need help. PLease if anyone can help, it would be very appreciated. Thank you.
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a) What is d, the difference between any 2 terms?
Answer:
Show work in this space.
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space.
Click here to see answer by kathysmiles77777(4) |
Question 39248: did I do this right: Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer: r=3
Show work in this space.
each are multiples of 3
1*3=3, 3*3=9, 9*3=27 and so on
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer:n=19683
Show work in this space.
a(n)=a(1)(r^n-1)
a(n)=1(1)*(3^10-1
a(n)=3^9=19683
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer: s=29524
Show work in this space.
s(n)= a(1)(1-r^n)/1-r
s(n)= 1(1)*(1-3^10)/(1-3)=29524
Click here to see answer by fractalier(6550) |
Question 39346: I asked this question before, but I did not get all the parts to the uestion posted for some reason. So please help. This includes all the parts, plus some of the answers if my answers are correct. Thanks a bunch.
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a) What is d, the difference between any 2 terms?
Answer: d=4
Show work in this space. work below
The value of the 20th term, i.e., when n=20, is found by using the general term: for a=3, d=4, and n=20, its value is 3+(20−1)4=79
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
B.sequences
To find the value of the nth term in an arithmetic sequence, use the following equation:
an = a1 + (n–1)d
a is the standard variable used to represent a term in a sequence and n counts the term number, so an represents the term in the sequence that you’re trying to find. d is the constant. To solve the problem, just substitute 101 for n, –3 for a1, and 5 for d.
a101 = -3 + (101 – 1)5
a101 = 497 part B
c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer: The sum of the first 29 terms would be 79
Show work in this space.
work above.
d) Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space.
e) What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer:
Click here to see answer by longjonsilver(2297)  |
Question 39348: Please help again, appreciate any and all help.
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: the sum of the first 10 terms is: 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
Click here to see answer by longjonsilver(2297) |
Question 39310: Need help solving assingment due tongiht.
1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following:
a) What is d, the difference between any 2 terms?
Answer:
Show work in this space.
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.
c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space.
d) Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space.
e) What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer:
Click here to see answer by venugopalramana(3286) |
Question 39308: Need help solving assignment due tongiht.
2) Use the geometric sequence of numbers 1, 3, 9, 27, … 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 nth term of a geometric sequence, what is the 10th 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.
Click here to see answer by venugopalramana(3286) |
Question 39453: Please help. I do not understand at all. Thanks for all the help.
Details: Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally
Click here to see answer by Nate(3500) |
Question 39485: Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.
Click here to see answer by stanbon(75887) |
Question 39455: Please help.
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: the sum of the first 10 terms is: 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.
Click here to see answer by stanbon(75887) |
Question 39454: Please help.
2) Use the geometric sequence of numbers 1, 3, 9, 27, … to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer: the sum of the first 10 terms is: 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.
Click here to see answer by venugopalramana(3286) |
Question 39508: I really need some help!! (Fast!!!!) Please....
Using the index of a series as the domain an dthe value of the series as the range, is the series a function?
Include in ans:
Which one of the basic functions(linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real life examples of both arithmetic and geometric sequences and series. Explain how these might affect you personally?
2. Use the arithmetic sequence of numbers 2,4,6,8,10...to find the following:
a) What is d, the difference between any 2 terms?
Ans:
Show work below:
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Ans:
c) Using the formula for the sum of an aritmetic series, what is the sum of the first 20 terms?
Ans:
d) Using the formula for the sum of an aritmetic series, what is the sum of the first 30 terms?
Ans:
e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc..)?
Click here to see answer by venugopalramana(3286) |
Question 39188: I am not sure if this question is in the proper place, but somebody please help. I do not understand.
Using the index of a series as the domain and the value of the series as the range, is a series a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
Give real-life examples of both arithmetic and geometric sequences and series. Explain how these examples might affect you personally.
Click here to see answer by venugopalramana(3286) |
Question 39635: 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 Crane came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Crane 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 grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat.” As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
a)How much wheat would Mr. Brown have to put on the 24nd square?
Show work in this space.
b)How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Show work in this space
c)Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
Answer:
Click here to see answer by venugopalramana(3286) |
|
Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790
|
