Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 405300: I really need help with this question, I would appreciate any input, thankyou!
A culture of bacteria has 20 cells in it. The number of cells doubles every 30 minutes. Write the first 5 terms of this sequence and explain where this sequence is arithmetic or geometric and justify your answer.
Click here to see answer by stanbon(75887)  |
Question 408537: The sum of the first two terms of a seven-term GP (geometric progression) is 20 and the sum of the last two terms is -5/8. Find the sum of all seven terms.
I know that a GP is one in which the ratio obtained by dividing any term by the preceding term is always the same. I also know the formula for finding the nth term in a geometric sequence. The first thing I tried was to let x = the first term. Then (20 - x) = the second term. Additionally, I let y = the next to the last term and (-5/8 - y) = the last term. Since the ratio by dividing any term by the preceding term is always the same, I have:
(20 - x) / x (ratio of 2nd term to 1st term)
(-5/8 - y) / y (ratio of 7th term to 6th term)
I set the equal to each other because the ratios are required to be the same in a GP:
(20 - x) / x = (-5/8 - y) / y
20y - xy = (-5/8)x - xy
20y = (-5/8)x
y = (-1/32)x
OR solving the same equation for x gives: x = -32y
From this point I thought about trying to just choose numbers either for x or y and then use the given common ratio to find the rest of the terms, but it didn't work out. Can you provide me with a step-by-step solution to this intriguing question? Thank you.
Click here to see answer by stanbon(75887) |
Question 410797: I have to find the "nth" term in a sequence. The series of numbers is -2,-10,-50, -250... I have to find the fifth and ninth term in this sequence. I have come across several equations and they are:
 and 
This is a question on a take home quiz and don't necessarily want the answer, I just need help on what each of the variables stands for.(Example: A(n) is the nth term you want to find)
Please help A.S.A.P. and Thank You!
Sincerely,
-In Need of Help
Click here to see answer by scott8148(6628)  |
Question 410797: I have to find the "nth" term in a sequence. The series of numbers is -2,-10,-50, -250... I have to find the fifth and ninth term in this sequence. I have come across several equations and they are:
and
This is a question on a take home quiz and don't necessarily want the answer, I just need help on what each of the variables stands for.(Example: A(n) is the nth term you want to find)
Please help A.S.A.P. and Thank You!
Sincerely,
-In Need of Help
Click here to see answer by stanbon(75887) |
Question 412077: Hello, can somebody please help me with this question I don't understand it
The 8th term of an arithmetic sequence is 25 and the 20th term is -11. Find the first term of the sequence and the common difference and use those to write the general term.
Click here to see answer by stanbon(75887) |
Question 412077: Hello, can somebody please help me with this question I don't understand it
The 8th term of an arithmetic sequence is 25 and the 20th term is -11. Find the first term of the sequence and the common difference and use those to write the general term.
Click here to see answer by Edwin McCravy(20056)  |
Question 417410: for each series, determine if the series converges or diverges. list at least the first 5 partial sums for each series. if the series converges, state the value. show graphical support for you conclusions.
infinite above sigma, k=1 under sigma, (1/(k-1!) on the side
Click here to see answer by richard1234(7193)  |
Question 417939: Can somebody PLEASE help me with this question, I have tryed to do it so many times, but just can't seem to figure it out. Any help would be appreciated!:)
a.)For the sequence 0,3,8,15,24....what would be the next three terms?
b.)What would be the function f(x) that would correspond to this sequence?
c.)what would the genera term tn for the nth term of this sequence be?
d.)How would you describe this sequence recursively, and write a recursive formula for this sequence?
e.)How would you find the 13th term of this sequence, using your formula from b.?
Click here to see answer by stanbon(75887) |
Question 419071: 1. How may different ways can a president, vice president, and secretary be chosen from a clum with 10 members? I am thinking that its 30, but not sure.
2. How many 4 letter codes can be formed with the letters A, B, C, D, E, F, G, H with repetition?
Thanks
Click here to see answer by sudhanshu_kmr(1152)  |
Question 420655: Having just taken a year of Algebra, Algebra II and College Algebra, my Statistics class is now using Summation, which was never covered in my algebra classes. One question which I do not understand is:
Why is: Sigma x^2 different from (Sigma x^2)? given the following values for x: 1,7,0,8, -6
The answer given me was non parenthesied answer is 150, parenthesied answer is 100.
Click here to see answer by stanbon(75887) |
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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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