Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 64423: 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?
Click here to see answer by Edwin McCravy(20056)   |
Question 64422: 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 you make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?
Click here to see answer by Edwin McCravy(20056) |
Question 64676: I am having problems with this. I think I have figured out the first one. Thanks in advance for any help.
Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any 2 terms?
Answer: d = 2
Show work in this space.
1 +2 =3 + 2 =5 + 2 = 7 etc.
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.)? Express your observations as a general formula in "n."
Answer:
Click here to see answer by stanbon(75887) |
Question 65064: I am so lost on this. Please help....
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 stanbon(75887) |
Question 65514: Hello.
I have no idea how to solve the following problem. Apparently, our teacher forgot to go over it. I just need help on where to start. Perhaps you can give me an example?
The problem is as follows:
Simplify:
(n+3)! / (n+1)!
Thank you for your help.
Click here to see answer by stanbon(75887) |
Question 65739: Please help me figure out this word problem. Considering yourself, your parents, your grandparents, and so on, back to your grandparents with the workd "great" used in front 40 times. What is the total number of people that you are considering. Thanks for your help.
Click here to see answer by ntnk(54) |
Question 65739: Please help me figure out this word problem. Considering yourself, your parents, your grandparents, and so on, back to your grandparents with the workd "great" used in front 40 times. What is the total number of people that you are considering. Thanks for your help.
Click here to see answer by stanbon(75887) |
Question 65740: Another problem I need a little help with.
Find the sum of the infinite geometric series if possible.
-1+(1/4)-(1/16)+(1/64)....
I multiplied by 4 and came up with 4s=-4+1-(1/4)+(1/16). What do I do next? Or maybe it's not possible to find the sum.....???
Thanks
Click here to see answer by praseenakos@yahoo.com(507)  |
Question 65758: Please help me find the sum of this finite geometric series.
2+10+50+250+1250. So far I have a=2, r=5 and n=126. Using the formula
Ssubn=(a(1-4^n))/1-r, I have Ssub126=(2(1-5^126))/1-5. This is where things get out of hand. On my calculator I come up with 5.877x10^87. This is supposed to add up to 1562.
Click here to see answer by ptaylor(2198)  |
Question 65876: Regarding question #65739. The one about the number of people when counting yourself through your great grandparents using 40 "greats". Since the number obtained is roughly 1000 times the number of people that have ever lived, this is absurd. There must be something wrong with the reasoning. What is it?
Click here to see answer by Edwin McCravy(20056) |
Question 65997: here's the sequence/pattern:
1, -1, 2, -2, 3,....
how would u explain the pattern besides the fact that it goes in order and after the positive number you put the opposite of it?? or is that all?? or is some addition/subtraction involved??
Click here to see answer by Edwin McCravy(20056) |
Question 66248: I have a test coming up. I really need to know if I am on the right track.
1] list the first 4 terms of sequence given by the formula: s[n]=n!/n^2, n>=1.
I came up with 1, 1/2, 2/3, 3/2.
2} list the first 4 terms of sequence given by the recursion formula
a[n]=2a[n-1]+3, with a[1]=1. I came up with (1,3,7,15)
3] the sum of the first 500 terms of aritmetic series 1+4+7+...
I came up with 125,000
Click here to see answer by stanbon(75887) |
Question 66348: 16. Central high school is selling lottery tickets to raise money for a new sound system. There are 18 prizes for the lottery, and the students and teachers sold 2400 tickets.
A. what fraction of the people who bought tickets will win a prize?
B. what fraction of the people who bought tickets will not win a prize?
C. what is the probability that someone who buys one ticket will win a prize?
Click here to see answer by venugopalramana(3286) |
Question 66350: 2. Use the distributive property to rewrite each family of expressions without using parentheses. Enter (2, 5, 6) into list L1 and (-3.6, -0.5, 12) into list L2 on your calculator, and use them to check your answers numerically.
A. 3(L1 +2)
B. -4 (6 - L2)
C. -7 (L1 -3)
Click here to see answer by ptaylor(2198) |
Question 66564: Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost?
Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations.
Click here to see answer by stanbon(75887) |
Question 67569: 1)
Lets say that we have a tree. The first day the height of the tree is 1 meter. The second day is 50cm higher. (1.50m). The third day is 25cm higher(1.75m)The fourth day is 12.5cm higher. The next day is 6.25cm higher, next day is 3.125cm higher and so on. Make a Sigma notation that will show the height of the tree after n days...
2)
The leaves of the tree are:
first day=1
second day=3
third day=7
fourth day=15
fifth day=31
sixth day=63
seventh day=127
day8= 255 leaves and so on......
A sigma notation that will give the number of leaves after n days....
Thank you in advance
Click here to see answer by aaaaaaaa(138) |
Question 67596: 1) find two consecutive odd integers whose product is 143
2) a rectangle is 4 cm longer than it is wide, and its area is 117cm squared. find its dimensions
3)the area of a right triangle is 44m squared. find the lenghts of its legs if one of the legs is 3 m longer than the other
4) the hypotenuse of a right triangle is 25 m long. the length of one leg is 10m less than twice the other. find the length of each leg.
please show your work
thank you
Click here to see answer by checkley71(8403) |
Question 67603: 1) the area of a right triangle is 44m squared. find the lengths of its legs if one of the legs is 3 m longer than the other
2) the hypotneuse of a right triangle is 25m long. the length of one leg is 10m less than twice the other. find the length of each leg.
please show your work
thank you very much!!!!!
Click here to see answer by stanbon(75887) |
Question 67665: I am working with recursive functions. I do not understand the examples given in the book.
Example 1 is evaluating a recursive function. Use the following defintion to find the value of f(4).
f(1)=3 and f(n)= f(n-1) + n
solution:
f(1)=3
f(2)= f(1)+2=3+2=5 This is where I get lost.
f(3)=f(2)+3=5+3=8
f(4)=f(3)+4=8+4=12
I understand factorals but this I do not understand. Also is there a website that would guide me slower through the recursive functions?
Thank you
Kate
Click here to see answer by stanbon(75887) |
Question 67698: Thanks for responding to my question. I understand what you were doing but I am still confuse about where the other equation works in f(n)= f(n-1)+n. Some other problems have this equation changing. ie: f(n)= f(n-2) + f(n-1) and f(0)=1
Kate
Click here to see answer by stanbon(75887) |
Question 68836: Please help. I tried to figure this problem out, but I couldnt.
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. Crane have to put on the 24th 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 68833: I can't figure this out. Please help.
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 rmromero(383) |
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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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