Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

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Question 1199651: The sum of the first four terms of a linear sequence A.p is 26 and that of the next four term is 74. find the value of the first term ,the common difference
Click here to see answer by MathTherapy(10552)

Question 1199753: I've been trying to understand a solution by greenstamps here:
https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1132971.html
He got me started by giving the rationale, but when I got to work on it, I didn't get the same answer as him and I have no idea why. Here's my work:
Q)
100, 101
100 + 101 = 201
100, 101, 201
201 + 100 = 301
201 + 101 = 302
100, 101, 201, 301, 302
301 + 100 = 401 GOOD
301 + 101 = 402 BAD
100, 101, 201, 301, 302, 401
401 + 100 = 501 GOOD
301 + 201 = 502 BAD
302 + 201 = 503 GOOD
100, 101, 201, 301, 302, 401, 501, 503
501 + 100 = 601 GOOD
501 + 101 = 602 BAD
503 + 100 = 603 BAD
503 + 101 = 604 GOOD
100, 101, 201, 301, 302, 401, 501, 503, 601, 604
SUM = 3,615
Exactly 200 more than what he got.
Where am I wrong?
Please help. Thanks!

Click here to see answer by greenestamps(13200)

Question 1199870: find the sum of the proper divisors of 141 158 161
Click here to see answer by ikleyn(52788)

Question 1199870: find the sum of the proper divisors of 141 158 161
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Question 1200167: I know the chosen topic has nothing to do with this but I couldn’t find the topic for this problem.
Use polynomial identities and number properties to perform the calculation.
109^2
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Question 1200258:
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Question 1200258:
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Question 1200344: If geometric series 2,5+7,5+22,5+…=664300 determine the number of terms in the series
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Question 1200344: If geometric series 2,5+7,5+22,5+…=664300 determine the number of terms in the series
Click here to see answer by ikleyn(52788)

Question 1200343: For which values of n is the terms value equal to the sum of the terms to that point in the
The arithmetic sequence ; 7,5,3
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Question 1200343: For which values of n is the terms value equal to the sum of the terms to that point in the
The arithmetic sequence ; 7,5,3
Click here to see answer by greenestamps(13200)

Question 1200379: what is the common differance of 1/2, 1/3, 1/6, 0
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Question 1200418: If (3-x),6 and (7-5x) are in g.p find the common ratio and sum of g.p

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Question 1200418: If (3-x),6 and (7-5x) are in g.p find the common ratio and sum of g.p

Click here to see answer by greenestamps(13200)

Question 1200443: The numbers below have been put in order:
COmplete the missing numbers:
1. 42 57 ? 74 ?
2. 75 ? 124 ? 189
3. 82 ? ? 98 ? 142
4. 93 ? 65 ? ? 21
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Question 1200450:
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Question 1200503: A ball starting from rest rolls down an inclined plane and passes over 3 in. during the 1st second, 5 in. during the 2nd second, 7 in. during the 3rd second, etc. In what time from the rest will it cover 120 inches?
Click here to see answer by ikleyn(52788)

Question 1200509: find the 24th term of the arithmetic sequence whose common difference is d=2 and whose first term is -30

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Question 1200509: find the 24th term of the arithmetic sequence whose common difference is d=2 and whose first term is -30

Click here to see answer by greenestamps(13200)

Question 1153200: Consider the arithmetic series 3+7+11+15+19+23+27+...and answer the questions which fo.
(a) T1= S1=
(ii) express T1 in terms of S1
(b) T2= S2=
(ii)Express T2 in terms of S2 and S1
Click here to see answer by 02022256164089(1)

Question 1200515: Find the arithmetic sequence which has the sum of its n terms equal to 2n^2+3n
Thank you
Click here to see answer by ikleyn(52788)

Question 1200515: Find the arithmetic sequence which has the sum of its n terms equal to 2n^2+3n
Thank you
Click here to see answer by math_tutor2020(3817)

Question 1200598: The sum of five terms of an AP is 10 and the sum of their squares is 380. Find the first term and the common difference.
PLease Help me i have exams tommorow please
Click here to see answer by ikleyn(52788)

Question 1200599: a1=5
a2=5
an=2an-2
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Question 1200704: do you think your formula in 2c above would hold for a geometric series as wel
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Question 1200760: A G.P has 8 terms it first and last term are 0.3 and 38.4 calculate
(a) the common ratio
(b) the sum of the terms in the G.P
Click here to see answer by Edwin McCravy(20056)

Question 1200786: True or False
The associated series of an arithmetic sequence is also an arithmetic sequence.
Click here to see answer by ikleyn(52788)

Question 1200806: How do I classify the following sequences?
a. r-5, 5, r+5, ... ... ...
b. p, p^2-1, P^3-2p+1/p, ... ... ...
Click here to see answer by ikleyn(52788)

Question 1200806: How do I classify the following sequences?
a. r-5, 5, r+5, ... ... ...
b. p, p^2-1, P^3-2p+1/p, ... ... ...
Click here to see answer by greenestamps(13200)

Question 1201145: Adam’s annual salary is RM120,000 and his total expenses is RM90,000. His salary increases
by RM12,000 each year while his expenses increase by RM15,000 each year. Each year, he
saves the excess of his income.
a) Represent his total savings as series.
b) If Adam continues to manage his finances this way, after how many years will he has
nothing left to save?
c) Adam calculates that if his expenses increase by 𝑥 RM every year (instead of RM15,000
each year), he will spend as much as he earns in the 25th
year. Determine 𝑥.

Click here to see answer by mananth(16946)

Question 1201229: A man is able to save #50000 of his salary in particular year. after every year he saved #20 more than the preceding year.
How long does it takes him to save #4370.

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Question 1201437: you and your parents are working on a scrapbook representing your family tree. He would like to include one page for the biography of each and sister, and your parents want you to include a page on yourself, classify the number of ancestors in each generation, as an arithmetic or geometric sequence.

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Question 1201463: Idk if that's the right title subject for my dilemma. Trying to find the missing number in the sequence. The sequence is as follows;
10|?|41|17|52|09
Find the missing number(?) In the sequence.
I am stumped and now just asking random places for the answer.
Please and thank you.

Click here to see answer by ikleyn(52788)

Question 1201483: Please help me with this problem. Thank you in advance
Write the recursive rule for 0,3,0,3,0,3....
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Question 1201544: 1/2 +1/8 +1/32 +...+1/2^2n-1
Need to find the limit. Please help.

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Question 1201651: An arithmetic sequence of 15 terms has a sum of 3060. The common difference and each member of the arithmetic sequence are all positive even integers. If a is the first term of any such arithmetic sequence, find the sum of all distinct a in which at least one of the first four terms of the arithmetic sequence is the square of an integer.
Click here to see answer by greenestamps(13200)

Question 1201664: Please help me with this problem

Write a rule for the nth term of the arithmetic sequence where
𝑎4 = 14 and 𝑎10 = 47
Click here to see answer by josgarithmetic(39618)

Question 1201664: Please help me with this problem

Write a rule for the nth term of the arithmetic sequence where
𝑎4 = 14 and 𝑎10 = 47
Click here to see answer by ikleyn(52788)

Question 1201718: If the first term of a sequence is 6,
the second is 30 and the fourth is 78,
what is the fifth term?
A) 30
B) 84
C) 102
D) 108
E) 114
Click here to see answer by ikleyn(52788)

Question 1201742: Please help me with this problem:
Write a rule for 1, 1/2, 3, 1/4, 5, 1/6, 7....
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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