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

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Question 1132100: The sum of the first three terms of a G.P. is 42 and the fourth term exceeds the first by 42.
Find the values of the first term and the common ratio.
Click here to see answer by math_helper(2461)

Question 1132178: 2, 3, 6, 0, 10, -3, 14,
Click here to see answer by Alan3354(69443)

Question 1132228: can you solve the next number in this sequence:
-1, 6, 25, 62,
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Question 1132268: The starting salary of a worker in a certain company is 2000000 shillings per annum. If annual increment is 30000 shillings. What is the total amount of money earned by the worker for twenty years?
Click here to see answer by ikleyn(52787)

Question 1132322: The numbers 3 and 192 are somewhere (but it is not known where) in a geometric sequence where all the terms in between are whole numbers. Find all the possibilities for the sequence.
I have found all 12 of the possibilities. They are:
2^6, 2^3, 2^2, 2^2, 2^1, 2^-6, 2^-3, 2^-2, 2^-1, -2^-2, -2^-1, -2^2 and -2^1
Solve the same problem with 5 and 3645. Explain why there are the same number of answers as
before.
I know the answer's for this question are the ones as before, but the Base for all of them are 3. So its:
3^6, 3^3, 3^2, 3^2, 3^1, 3^-6, 3^-3, 3^-2, 3^-1, -3^-2, -3^-1, -3^2 and -3^1
My question is that I need to know why they have the same amount of answers. If possible, I would like a step by step on how you got your answer. Thank you very much!
Click here to see answer by greenestamps(13200)

Question 1132351: insert seven arithmetic means between 2 and 26
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Question 1132438: The sum of three numbers in Ap is 39 and the sum of their product is 2184.find the number
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Question 1132438: The sum of three numbers in Ap is 39 and the sum of their product is 2184.find the number
Click here to see answer by ikleyn(52787)

Question 1132438: The sum of three numbers in Ap is 39 and the sum of their product is 2184.find the number
Click here to see answer by greenestamps(13200)

Question 1132426: Write the first five terms of the arithmetic series in which the sum of the second and ninth terms is 25, and the sum of the third and seventh terms is 20.
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Question 1132502: A pile of logs contains 20 logs on the topmost layer and each lower layer contains one more log than the above layer. If there are 25 layers in the pile, how many logs are there in all?
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Question 1132485:
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Question 1132635: A business director awards his staff with gift cards of $10.00 value each. He gives 3 gift cards to employees who have been employed in his business for 3 years, 5 gift cards to employees who have worked there for 5 years, and 10 gift cards for employees working there for 10 years. He gives out a total of 282 gift cards.
He has 14 more employees that working there for 3 years, than for 5 years. Also there are 3 fewer employees who have been working there for 10 years than for 5 years.
How many employees have been working there for 10 years?

Click here to see answer by ikleyn(52787)

Question 1132681: The first term of an arithmetic progression is -8.The ratio of the 7th term to the 9th is 5:8. Calculate the common difference
Click here to see answer by MathLover1(20850)

Question 1132711: One of the athletes could double his profit by 3 times at each of the seven stages of the competition he could overcome. Write down the sequence that represents the winner's profit at each stage, then find the general term if you know that what he earned in the first stage is 100 dollars.
Click here to see answer by stanbon(75887)

Question 1132827: Find the 20th term of the AP: 80, 75, 70,…and calculate the number of terms required to make the sum equal to zero
Click here to see answer by Alex.33(110)

Question 1132892: 10, 20, 17, 12, 19, 13, 15, 19, 13, 14, ?
Click here to see answer by ikleyn(52787)

Question 1132939: Sn=a(subscript1)x(1-r^n/1-r) is the formula if given are positive= 1/9+8/9+etc.
But what if the given are negative= -1-8-64-512...-(8)^n-1 or subtraction. Is the formula the same? or do is it flip and turn int0 a1x(1+r^n/1+r)?
Click here to see answer by MathLover1(20850)

Question 1132971: In the sequence 1,4,5,6,7,8,10,16,18,... each number after the first two is the next number that can be expressed as the sum of two previous numbers in only one way. For example, 10 is included because 6+4 = 10, and there is no other sum of two numbers in the sequence that equals 10. The number 15 is not included because both 10+5 and 8+7 equals 15. In a similar sequence that begins with the two numbers 100 and 101, the sum of the first ten terms is...
A)3515 B)3417 C)3216 D)3516 E)3415
Click here to see answer by greenestamps(13200)

Question 1133133: Select the option for "?" that continues the pattern in each question. 3, -6, 12, 4, 20, ?
Click here to see answer by Alex.33(110)

Question 1133165: 8;18;30:44
Calculate the nth term

Click here to see answer by MathLover1(20850)

Question 1133165: 8;18;30:44
Calculate the nth term

Click here to see answer by greenestamps(13200)

Question 1133314: The nth term of a sequence is donated by 3n (2n - 1)find the sum of the first five term
Click here to see answer by rothauserc(4718)

Question 1133314: The nth term of a sequence is donated by 3n (2n - 1)find the sum of the first five term
Click here to see answer by ikleyn(52787)

Question 1133418: Σn=1 2/(n(n+1))
ITS AN INFINITE SERIES AND STARTS AT 1.
Click here to see answer by ikleyn(52787)

Question 1133605: 1;3;5 are the first terms of the first difference of a quadratic sequence.
The 7th term of the quadratic sequence is 35.
1.determine the 6th and 5th terms of the quadratic sequence.
2.determine the nth term of the quadratic sequence.
Click here to see answer by MathLover1(20850)

Question 1133804: This boy gets this girl 1 Rose in one day the second day he gives 6 roses. what sequence is this what does it grow by? How many roses will the boy give on the 28th day? Can there be one day where the boy gives 100 roses how justify your answer. Thank you.

Click here to see answer by Alan3354(69443)

Question 1133988: Find the sum of the series 1/2+(1/3+2/3)+(1/4+2/4+3/4)+...+(1/100+2/100+3/100...+99/100).
Click here to see answer by greenestamps(13200)

Question 1134022: 2 ,3 ,7 ,29,?,3729
Click here to see answer by greenestamps(13200)

Question 1134278: The sixth & eleventh terms of a linear sequence are respectively 23 & 48. Calculate the sum of the first twenty terms
Click here to see answer by ikleyn(52787)

Question 1134278: The sixth & eleventh terms of a linear sequence are respectively 23 & 48. Calculate the sum of the first twenty terms
Click here to see answer by greenestamps(13200)

Question 1134277: The first term of an Ap is-1 and the sum of the first twenty terms is -240 .find the third term
Click here to see answer by greenestamps(13200)

Question 1134362: 0,1,A,B,C,5,D,E,F,G,H,89
Click here to see answer by Alan3354(69443)

Question 1134362: 0,1,A,B,C,5,D,E,F,G,H,89
Click here to see answer by greenestamps(13200)

Question 1134390: The sum of 8th terms of an AP is 160 while the sum of 20 terms is 880. Find (a) the 43rd term (b) the sum of 12 terms.
Click here to see answer by greenestamps(13200)

Question 1134391: The 28th term of an AP is -5. Find the common difference if its first term is 31.
Click here to see answer by greenestamps(13200)

Question 1134391: The 28th term of an AP is -5. Find the common difference if its first term is 31.
Click here to see answer by ikleyn(52787)

Question 1134389: The sum of money shared among nine people so that the first gets 75, 000, the next 150, 000, the next 225, 000, and so on. (a) How much money does the ninth person get? (b) How much money is shared altogether?
Click here to see answer by greenestamps(13200)

Question 1134480: I need to know the next nine numbers in the following sequence :
2,12,3,13,10,16,6,7,1...... Can anyone help please ?
Click here to see answer by ikleyn(52787)

Question 1134464: A computer prints all of the integers from 1 to 3456. How many times does it print the integer 5?
Click here to see answer by ikleyn(52787)

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