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

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Question 1191250: What is the smallest positive integer x for which the sum x + 2x + 3x +...+ 60 is a perfect square?
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Question 1191246: What is the sum of 1 - 2 + 3 - 4 + 5 - ... + 399 - 400?
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Question 1191254: The sequence 2, -4, a , and b is such that the first three terms form an arithmetic sequence and the last three terms form a geometric sequence. What is the values of a and b?
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Question 1191248: What is the arithmetic mean (ordinary average) of the 73 successive positive integers, starting with 5?
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Question 1191251: What is the sum of the following infinite series: (1/6) + (13/6^2) + (19/6^3) + (97/6^4) + ... + ((3^n) + (-2)^n) / (6^n)
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Question 1191256: What is the first of 100 consecutive odd integers whose sum is 100^100?
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Question 1191255: The roots of (x^3) + 2p(x^2) - px + 10 = 0 are integral and form an arithmetic sequence. What is the value of p?
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Question 1191255: The roots of (x^3) + 2p(x^2) - px + 10 = 0 are integral and form an arithmetic sequence. What is the value of p?
Click here to see answer by greenestamps(13200)

Question 1191253: the kth term of a sequence is given by the functions (3^k) - 2k + 2. What is the sum of the first ten terms?
Click here to see answer by MathLover1(20850)

Question 1191253: the kth term of a sequence is given by the functions (3^k) - 2k + 2. What is the sum of the first ten terms?
Click here to see answer by greenestamps(13200)

Question 1191247: By adding the same constant to each of the numbers 16, 32, and 56, respectively, a geometric sequence is formed. What is the common ratio for this sequence?
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Question 1191284: The sum to infinity of a geometric series is 8, whereas the sum of the second and third terms is 3. What are all the possible values of the common ratio of the series?
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Question 1191407: Find the sum of AP whose first term is 60 and last term is -104
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Question 1191427: For an arithmetic series , consisting of 15 terms,Sn=2n-n^2
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Question 1191495: In a given sequence the first term is 3, the last term is 58, and the sum of all the terms is 366. What is the common difference?
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Question 1191491: If 400 more than the sum of p consecutive integers is equal to the sum of the next p consecutive integers, what is the value of p?
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Question 1191494: What is the sum of all the integers between 40 and 440 which end in 3?
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Question 1191493: What is the sum of the infinite series whose nth term is:
(7^(n-1)) / (10^n)
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Question 1191492: If the sum of the first 10 terms and the sum of the first 100 terms of a given arithmetic progression are 100 and 10, respectively, then what is the sum of the first 110 terms?
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Question 1191490: Calculate the sum:
1/4(1^3) + 1/9((1^3) + (2^3)) + 1/16((1^3) + (2^3) + (3^3)) +...+ 1/2704((1^3) + (2^3) + (3^3) +...+ (51^3))
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Question 1191488: For p = 1,2,3,...,10 let S_p be the sum of the first 40 terms of the arithmetic progression whose first term is p and whose common difference is 2p-1. What is the value of S_1 + S_2 +...+ S_10?
Click here to see answer by greenestamps(13200)

Question 1191594: For the arithmetic sequence 2,3,5
Please help me to prove that none of the terms are perfect squares
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Question 1191585: A G.P has the second term as 9 and the fourth term is as 81.find the some of the first four term?
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Question 1192001: Arithmetic Series Question:
Determine the number of terms in the following arithmetic sequence.
2x + y, 3x + 4y, 4x + 7y,...10x + 25y
Textbook answer is 10.
Can someone please tell me how to get 10? Thank you.
Click here to see answer by josgarithmetic(39618)

Question 1192010: 27,-9,3,-1,

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Question 1192010: 27,-9,3,-1,

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Question 1192011: 27,-9,3,-1,
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Question 1192020: An oil company bores a hole 80ksh deep estimate the cost of boring the hole if the cost is 30ksh for drilling the first meter with an increase in cost of 2ksh per meter for each succeeding meters
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Question 1192405: I would like to understand number sequence
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Question 1192452: Is the sequence 2,4,8,16... arithmetic or geometric?
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Question 1192583: 07,70,23,23,72,99,47,?
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Question 1192584: 52,99,33,74,07,70,23,23,72,99,47,?
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Question 1192591: 07,70,23,23,72,99,47,?

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Question 1192621: 01,70,23,23,72,99,47,66,?
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Question 1193024: Use your formula in 2 c above to determine the value of t5
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Question 1193484: The number of trees damaged reported over a four year period 20, 41,83,167 Find the recursive formula
and predict how many trees will be damaged in the seventh year if this trend continues?

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Question 1193491: Find the sum of this series that is not arithmetic or geometric,
1+2+4+5+7+8....+95+97+98
Click here to see answer by Alan3354(69443)

Question 1193479: For the sequence 2,-2,4,-6,10.... find the recursive formula

Thank you
Click here to see answer by Edwin McCravy(20056)

Question 1193479: For the sequence 2,-2,4,-6,10.... find the recursive formula

Thank you
Click here to see answer by ikleyn(52788)

Question 1193479: For the sequence 2,-2,4,-6,10.... find the recursive formula

Thank you
Click here to see answer by greenestamps(13200)

Question 1193516: Find the number of terms in this geometric series
-4 + 16 - 64 + 256..., where Sn=52428

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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