Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 1028162: Can you explain how to solve a problem that would ask the total amount of money a worker would receive after working at a company for 40 years and received a 3% raise every year with a starting salary of $40,000 a year?
Click here to see answer by addingup(3677)   |
Question 1028342: Could someone please check my work? I am supposed to label each statement as True or False, and if False, replace the words in all caps to produce a true statement.
1) A sequence is a function whose domain is A SUBSET OF THE INTEGERS. I chose False because my book states "a set of consecutive integers".
2) A sequence can be defined EITHER EXPLICITLY OR IMPLICITLY. I think this is true because a sequence can be clearly stated or implied.
3) The sum of an infinite geometric series is finite only if THE ABSOLUTE VALUE OF THE COMMON RATIO IS LESS THAN ONE. I think this is true.
I appreciate any help!
Click here to see answer by ikleyn(52788)  |
Question 1028411: Could someone please check these and tell me if my answers are correct? I would appreciate it very much, I don't feel confident with my answers!
1) Find the sum of all of the 3-digit positive integers.
my answer: (999(99+1))/(2) - (99(99+1))/(2)
(999(1000))/(2) - (99(100))/(2)
(999(500)) - (99(50))
499500 - 4950 = 494550*****
2) Find the sum of every integer from 1 to 1000 that is not a perfect square.
my answer: ((1000)(1000+1))/(2)
(500)(1001)
500500*****
Click here to see answer by Alan3354(69443)  |
Question 1028586: Could someone please check my answers? I am supposed to write both a recursive and an explicit rule that will generate the values in the table, provided that a"subscript"o=3/2
n--------------1-----2-----3-----4------5-------6
a*sub*n------2-----3-----5-----9-----17-------33
Recursive rule= a"sub"o= 3/2, a"sub"n=a"sub"(n-1) +2 "super" n-2
Explicit rule= a"sub"n=3/2+1/2(2"super"n-1)
I hope this makes sense, I don't know how to make the subscripts on my keyboard. I appreciate any help!
Click here to see answer by Fombitz(32388)  |
Question 1028744: Harper buys a car in 2007 for $20000. Each year,the car decreases in value by 18%. How much will the car be worth in 2012? round to the nearest cent.
What's the common ratio?
I got it as 0.18. Is that correct?
Click here to see answer by Theo(13342)  |
Question 1029187: Using algebraic progression:
Hanh deposited $200 into the bank on 1 January and on the first day of each of the following months. At the end of June, when the interest was calculated, he found that his account balance was $1206.30. Find the rate of simple interest paid by the bank.
Click here to see answer by stanbon(75887) |
Question 1029361: An object is projected vertically upwards from the ground with sufficient initial force to make it rise 105 metres in the first seconds of its flight. It travels 95 metres in the second second, 85 metres in the third seconds and so on.
a) How long does it take the object to reach its greatest height above the ground:
This is what I have so far:
I have interpreted that the greatest height above the ground must be when
Tn = 0 (or in other words at the second the object is travelling 0 metres)
I have worked this out to be 11.5 seconds, where I have used
Tn = a + (n-1) d
where n= 11.5
I have stated that although n must be an integer, in this context n refers to seconds and thus decimals are allowed. I am not sure whether this is correct.
Also the correct answer is 11 seconds, so I am a bit confused as to how this answer is obtained, as wouldn't the object would still be travelling upwards at 11 seconds and thus the greatest height above the ground wouldn't have been reached.
Thankyou for your help.
Click here to see answer by Alan3354(69443) |
Question 1029361: An object is projected vertically upwards from the ground with sufficient initial force to make it rise 105 metres in the first seconds of its flight. It travels 95 metres in the second second, 85 metres in the third seconds and so on.
a) How long does it take the object to reach its greatest height above the ground:
This is what I have so far:
I have interpreted that the greatest height above the ground must be when
Tn = 0 (or in other words at the second the object is travelling 0 metres)
I have worked this out to be 11.5 seconds, where I have used
Tn = a + (n-1) d
where n= 11.5
I have stated that although n must be an integer, in this context n refers to seconds and thus decimals are allowed. I am not sure whether this is correct.
Also the correct answer is 11 seconds, so I am a bit confused as to how this answer is obtained, as wouldn't the object would still be travelling upwards at 11 seconds and thus the greatest height above the ground wouldn't have been reached.
Thankyou for your help.
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 1029361: An object is projected vertically upwards from the ground with sufficient initial force to make it rise 105 metres in the first seconds of its flight. It travels 95 metres in the second second, 85 metres in the third seconds and so on.
a) How long does it take the object to reach its greatest height above the ground:
This is what I have so far:
I have interpreted that the greatest height above the ground must be when
Tn = 0 (or in other words at the second the object is travelling 0 metres)
I have worked this out to be 11.5 seconds, where I have used
Tn = a + (n-1) d
where n= 11.5
I have stated that although n must be an integer, in this context n refers to seconds and thus decimals are allowed. I am not sure whether this is correct.
Also the correct answer is 11 seconds, so I am a bit confused as to how this answer is obtained, as wouldn't the object would still be travelling upwards at 11 seconds and thus the greatest height above the ground wouldn't have been reached.
Thankyou for your help.
Click here to see answer by rothauserc(4718)  |
Question 1030376: Tweve iron poles are to be used for pillars and the length of the poles for an arithmetic progression (AP). If the third pole is 4m and the seventh pole is 10m. Find the length of the poles inorder of AP and cost of all the poles if a meter cost $45.
Click here to see answer by ikleyn(52788) |
Question 1030735: Jeremy has a bag of peanuts. He is going to share them so he counts them out. First he uses groups of 2, then groups of 3, 5 and 8, but each time there is 1 peanut left. How many are in the bag? Is there more than one answer?
Please give me some ideas to solve this problem. Thanks !
Click here to see answer by mananth(16946)  |
Question 1030772: Hi. this lesson is really confusing me and I need help with it. These questions are confusing me. Please help me solve these problems.
For questions 3-5, find the first 4 terms and the 8th term of the recursively-defined sequence.
3. b1 = 2 and bk+1 = 3bk, for k>0
4. v1 = 0.75 and vn = (-2)vk-1 for n>1
5. c1 = 2, c2 = -1, and ck+2 = ck + ck+1 for k>0
6. Identify the sequence {-2, 2, -2, 2 ...} as arithmetic or geometric. Then find the common difference or ratio as appropriate.
7. Identify the sequence {-5, -2, 1, 4 ...} as arithmetic or geometric. Then find the common difference or ratio as appropriate.
8. The third and sixth terms of a geometric sequence are -75 and -9375 respectively. Find the first term, the common ratio, and an explicit rule for the nth term.
Click here to see answer by ikleyn(52788) |
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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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