Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 82554: Find the next term of the sequence.
1, 8, 27, 64, ...
What is the formula for the following arithmetic sequence?
-2, 3, 8, 13, ...
a.an = -2n + 3
b.an = -2n + 7
c.an = 5n + 3
d.an = 5n - 7
What is the common difference of the sequence?
2, -1, -4, -7, ...
Click here to see answer by 303795(602)  |
Question 82554: Find the next term of the sequence.
1, 8, 27, 64, ...
What is the formula for the following arithmetic sequence?
-2, 3, 8, 13, ...
a.an = -2n + 3
b.an = -2n + 7
c.an = 5n + 3
d.an = 5n - 7
What is the common difference of the sequence?
2, -1, -4, -7, ...
Click here to see answer by checkley75(3666) |
Question 82553: Write the equation of the arithmetic sequence defined by a1 = 3 and a4 = 0. (write your answer in the form an= and please do NOT use spaces)
What is the common ration of the sequence?
-2, 2, -2, 2, ...
What is the explicit formula for the sequence?
3, 6, 12, 24, ...
a. an = 3*2^(n-1)
b. an = 2*3^(n-1)
c. an = 3*-2^(n-1)
d. an = 3^(n-1)
Click here to see answer by stanbon(75887) |
Question 82551: pick right chioce for each thank u
Question 9
You can do 10 situps at the beginning of the month. You add 1 additional situp everyday. How may TOTAL situps have you done after 30 days?
a. 10
b. 30
c. 735
d. 1030
Question 10
You drive a 12 inch spike into a piece of wood 1/3 of the way with each strike of the hammer. How far has the spike gone into the wood (total) after the 3rd hit of the hammer? Round your answer to the nearest tenth.
a. 3.6 inches
b. 0.4 inches
c. 8.4 inches
d.12 inches
e. 11.6 inches
Click here to see answer by josmiceli(19441)  |
Question 82644: Find the sum of the first 10 terms of the series defined by the formula:
an = -2n + 5
a. 3
b. 2
c.-60
d. -15
A 5 inch spike is being pounded in to a log. Every time you hit the hammer 1/4 of the remaining spike goes into the log. What kind of sequence or series is definied by the total distance the spike goes into the log?
a. arithmetic sequence
b. arithmetic series
c. geometric sequence
d.geometric series
Click here to see answer by stanbon(75887) |
Question 82683: From the information in the table providing values of f(x) and g(x), evaluate (f . g ) ^ -1 (2).
x 1 2 3 4 5
f(x) 3 4 5 1 2
g(x) 5 4 2 3 1
The answer I came out with was 4. Could you confirm this for me? Thanks
Click here to see answer by stanbon(75887) |
Question 82690: A computer access-code number was designated in a special way. It was a 4-digit number. The nmber is the smallest integer that can be written as the sum of two positve cubes in two different ways, and the number is between 1000 and 2000. What is the code number?
Click here to see answer by kev82(151) |
Question 83206: Apply the formulas for motion due to gravitational attraction.
A stone is dropped from the top of a building 240 feet high. It is observed to take 0.20 seconds to go past an office floor-to-ceiling window that is 12 feet high. How far is it from the bottom of the window down to the street?
Click here to see answer by stanbon(75887) |
Question 83285: Question-2: A 100 grams of a radioactive substance is expected to decay exponentially to 50 grams in the course of 7 years.
(a) Write down the half-life, and the rate of decay of the radioactive substance.
(b) Write down the function N(t) representing the mass of the decaying radioactive substance after t years,
(c) How much of the substance is expected to remain after 14, 21, and 28 years, respectively?. How long would it take for the radioactive substance to decay to under 1 gram?.
Click here to see answer by stanbon(75887) |
Question 83716: We are having a lecture this afternoon and I would like to be able to apply the lecture to this so that I can understand it. Thanks for any help.
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any two consecutive 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 sequence, 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 sequence, 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 sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."
Answer:
Click here to see answer by stanbon(75887) |
Question 83716: We are having a lecture this afternoon and I would like to be able to apply the lecture to this so that I can understand it. Thanks for any help.
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any two consecutive 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 sequence, 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 sequence, 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 sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."
Answer:
Click here to see answer by jim_thompson5910(35256) |
Question 83790: Can you please assist me with the following problem?
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?
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?
Thank you for your help...
Click here to see answer by jim_thompson5910(35256) |
Question 83789: Can someone assist me with the following problem please?
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?
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
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.
d) What observation can make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?
Thank you for your assistance...
Click here to see answer by jim_thompson5910(35256) |
Question 83788: Please can you help me with the following problem.
Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Thank you for your help.
Click here to see answer by Nate(3500) |
Question 83820: Use the geometric sequence of numbers 1, 2, 4, 8,… to find the following:
What is r, the ratio between 2 consecutive terms?
Show work:
Using the formula for the nth term of a geometric sequence, what is the 24th term?
Show work:
Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Show work:
Click here to see answer by jim_thompson5910(35256) |
Question 83819: I've tried numerous times to get this right, but I can't figure it out.
Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?
Give at least two real-life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally.
Click here to see answer by jim_thompson5910(35256) |
Question 83722: Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
Include the following in your answer:
1. Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
2. Which one of the basic functions (linear, quadratic, rational, or exponential)is related to the geometric sequence?
3. Give at least two real-life examples of sequences or series. One example should be arithmetic, and the second should be geometic. Explain how these examples would affect you personally. The one thing I can think of is age, but I don't know how to put it correctly.
Click here to see answer by jim_thompson5910(35256) |
Question 83906: Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?
Give at least two real-life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally.
Click here to see answer by jim_thompson5910(35256) |
Question 83996: Is this correct?
Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
What is r, the ratio between 2 consecutive terms?
Answer: r = (1/2)/1 = 1/2
Show work in this space.
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.
S(n) = a(1)[r ^(n + 1) – 1)/(r – 1)
S(10) = 1[(1/2) ^ 9 – 1] / [(1/2)-1]
S(10) = [-0.998046875…] / [-0.5] = 1.99609375…
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.
S(n) = a(1)[r ^(n + 1) – 1)/(r – 1)
S(12) = 1[(1/2) ^ 9 – 1] / [(1/2)-1]
S(12) = [-0.998046875…] / [-0.5] = 1.99609375…
n = 12
Click here to see answer by jim_thompson5910(35256) |
Question 84018: Can someone assist me with the following problem please?
Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any two consecutive terms?
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term?
c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
e) What observation can you make about these sums of this sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."
Thanks so much for your help.
Click here to see answer by jim_thompson5910(35256) |
Question 84125: Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any two consecutive terms?
Answer: 2
Show work in this space.
1(3-5) =2
1(7-9) =2
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: 10,050.5
Show work in this space.
a =50.5+(101-1) (-100)=50.5+100(-100)=10,050.5
c) Using the formula for the sum of an arithmetic sequence, 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 sequence, 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 sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."
Answer:
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:
Show work in this space.
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
Click here to see answer by jim_thompson5910(35256) |
Question 84127: 1. Use the arithmetic sequence of numbers 1,3,5,7,9,....to find the following:
a. What is d, the difference between two consecutive terms?
show your work
**I am not sure what the teacher is asking here, but I think the answer is 1. 1+2=3+1=4+1=5 and so forth.
b. Using the formula for the n(th)term of an arithmetic sequence, what is the 101(st) term?
show your work
**Sn=n/2(a1+an) **I got 10,150.50
c.Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
show your work
**I got 400***
d.Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
show work
***I got 939***
e. What observation can you make about these sums of this sequence(HINT:It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n"
**I think the answer here is that the sequence of numbers goes up by one.
***Can you please help me, I want to make sure these answers are correct before I submit them.
Thank you so much for your time, I really appreciate it,
Jennifer
Click here to see answer by jim_thompson5910(35256) |
Question 84124: 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
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
Show work in this space
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:
Show work in this space
Click here to see answer by jim_thompson5910(35256) |
Question 84120: 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 whole number does it appear that the sum will always be smaller than?
Answer:
Click here to see answer by jim_thompson5910(35256) |
Question 84134: 1. Use the geometric sequence of numbers 1,2,4,8,...to find the following:
a. What is r, the ratio between 2 consecutive terms?
show work
***r=2/1=2
b. Using the formula for the nth term of a geometric sequence, what is the 24th term?
show work
***a n below=a, r 2-1 above
answer 615
c. Using the formula for the sum of a geometic series, what is the sum of the first 10 terms?
show work
****1,023.00****
Thank you for your help
Click here to see answer by stanbon(75887) |
Question 84139: Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
include in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
Which of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?
Give at least two real life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these would effect you personally.
Click here to see answer by jim_thompson5910(35256) |
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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
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