Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 1163812: Please dont give me an answer to the problem. I am not doing any homework. I am just learning (self educating). Just show me what is the approach. I know the formula for the sum of a sequence. But that on one side, and the given sum on the other side, I am stuck with solving the inequality and establishing a AP sequence.
Question: Find the arithmatic sequence which has the sum of its n terms equal to 2n^2+3n
Thank you
Click here to see answer by muthbab@gmail.com(5)  |
Question 1163863: Question: The sum of three numbers in a GP is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting sumber are in ARITHMETIC sequence. Find the Geometric sequence.
How far I got:
a + ar + ar^2 = 14 (1)
(a+1), (ar+1), (ar^2 - 1) = AP with sum of 15 (2)
Since the(2) is an AP:(ar+1) = [(a+1) + (ar^2 - 1)]/ 2
(ar+1) = [a(1+ar^2)]/2
2(ar+1) = a(1+ar^2)
Am I on the right path or does it need some other approach?
Than you
Click here to see answer by ikleyn(52788)  |
Question 1163889: Question: The first term of an arithmetic sequence is 2; and the first, third, and eleventh terms are also the first three terms of a geometric sequence. Find the sum of the first eleven terms of the arithmetic sequence.
How far I got:
The third term of AP: 2+2d which is equal to second term of GP 2r giving
equation (1)...... 2 + 2d - 2r = 0
Likewise, the 11th term of AP: 2+10d is equal to third term of GP 2r^2 giving
equation (2)...... 2 + 10d - 2r^2 = 0
Solving the system I get, r = 1 and 4 (discard 1 as it is GP) and d = 3
So the sum of AP is (34/2)= 17.
Obviously I am wrong. Can you please point it out.
Please dont give me the answer. Just give me the broad steps to solve the problem.
Thank you
Click here to see answer by greenestamps(13200)  |
Question 1163948: Question: The sum of the first two terms of a decreasing geometric series is 5/4, and the sum to infinity is 9/4. Write the first three terms of the geometric series.
I solved it. I dont need the answer. It was tedious, which is ok if that is the way to do it. But I need to know whether I am making it tedious because the way I approached it and whether I am missing another easier way to solve it!
The way I solved it was:
a + ar = 5/4 (1)
a/(1-r) = 9/4 (2)
Subtracting (1) - (2) gave me ar^2 (the third term) = 3/2
Dividing (1)/(2) gave me r= +/- (2/3) and in turn plugging the values gave me a=3/4.
(Then I realized that there was no need for the tedious subtraction!!)
Also can I assume 'dividing the sum of a geometric series by its sum to infinity will always yield r^2 '
Thank you
Click here to see answer by solver91311(24713)  |
Question 1163968: Question: “Find the 8th term of the harmonic sequence 2/3, ½, 2/5 …” (Quotation marks are mine)
I don’t need the answer. It is 1/5. I solved it after lots of frustration! I just need some clarification of mathematical wording and conventions that I should be familiar with.
Frustration:
I know the definition of harmonic sequence and the meaning of it being the inverse of an arithmetic sequence and all.
But, when they say explicitly “harmonic sequence 2/3, ½, 2/5 …” shouldn’t I assume that those three terms are already inverted. Why do I have to invert them? In other words, what wording will prompt me to know that they are being presented after the inversion or prior to inversion? Shouldn't the above problem be worded as "Find the 8th term of the harmonic sequnce of the following NUMBERS...".
Thank you
Click here to see answer by greenestamps(13200) |
Question 1164237: A geometric progression has 6 terms. The first term is 192 and the common
ratio is 1.5. An arithmetic progression has 21 terms and common difference 1.5.
Given that the sum of all the terms in the geometric progression is equal to the
sum of all the terms in the arithmetic progression, find the first term and the last
term of the arithmetic progression.
Click here to see answer by greenestamps(13200) |
Question 1164221: There is a Covid19 Pandemic in the world in Ghana it
affected 5 people on the first day. If Covid19 affects 2 people a day. How long
will take it 1,000,000 people to be affected in the country and also how many people will be affected on day 8 ?
Click here to see answer by ikleyn(52788) |
Question 1164220: There is a Covid19 Pandemic in the world in Ghana it
affected 5 people on the day. If Covid19 affects 2 people a day. How long
will take it 1,000,000 people to be affected in the country and also how many people will be affected on day 8 ?
Click here to see answer by ikleyn(52788) |
Question 1164214: When the terms of a Geometric Progression(G.P) with common ratio r=2 is added to the corresponding terms of an Arithmetic (A.P), a new sequence is formed. If the first terms of the G.P and A.P are the same and the first three terms of the new sequence are 3, 7, and 11 respectively, find the nth term of the new sequence.
Click here to see answer by greenestamps(13200) |
Question 1164214: When the terms of a Geometric Progression(G.P) with common ratio r=2 is added to the corresponding terms of an Arithmetic (A.P), a new sequence is formed. If the first terms of the G.P and A.P are the same and the first three terms of the new sequence are 3, 7, and 11 respectively, find the nth term of the new sequence.
Click here to see answer by jim_thompson5910(35256) |
Question 1164815: A theater has 50 seats in the first row, 58 seats in the second row, 66 seats in the third row, and so on in the same increasing pattern.
a. How many seats are there in the 4th and the 5th rows? Explain how you got your answer.
Click here to see answer by solver91311(24713) |
Question 1164850: -10, -7, -4, -1, 2, 5, 8, 11, 14, 17, 20. How to turn this into Sigma notation. Please
Click here to see answer by Edwin McCravy(20056)  |
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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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