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

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 1208497: 1/2, 2/3, 6/5,?
Click here to see answer by math_tutor2020(3817)

Question 1208630: find next number. 30,70,63,93,45,14,87,61,57,29,?
Click here to see answer by ikleyn(52787)

Question 1208641: If 1,1,3,9 be added respectively to four terms of an AP.,a GP results. Find the four terms of the AP
Click here to see answer by math_tutor2020(3817)

Question 1208641: If 1,1,3,9 be added respectively to four terms of an AP.,a GP results. Find the four terms of the AP
Click here to see answer by greenestamps(13200)

Question 1208674: The 10th and 15th terms of an AP are -5 and -15/2 respectively.what is the sum of the first 20 terms
Click here to see answer by greenestamps(13200)

Question 1208674: The 10th and 15th terms of an AP are -5 and -15/2 respectively.what is the sum of the first 20 terms
Click here to see answer by ikleyn(52787)

Question 1208760: Find an integer x such that when its divided over 5, 7, and 11 gives remainders 2,3, and 10

Click here to see answer by math_tutor2020(3817)

Question 1208795: 444, 456, 471, ? 498, 519
Click here to see answer by ikleyn(52787)

Question 1208795: 444, 456, 471, ? 498, 519
Click here to see answer by greenestamps(13200)

Question 1208795: 444, 456, 471, ? 498, 519
Click here to see answer by math_tutor2020(3817)

Question 1208816: If the 3rd term of a gp is four times its 5th term, find the possible values of the common ratio
Click here to see answer by ikleyn(52787)

Question 1208816: If the 3rd term of a gp is four times its 5th term, find the possible values of the common ratio
Click here to see answer by greenestamps(13200)

Question 1208833: (a)0.5+0.25+0.125+.....+9.765625 using formula (i)
Click here to see answer by ikleyn(52787)

Question 1208833: (a)0.5+0.25+0.125+.....+9.765625 using formula (i)
Click here to see answer by AnlytcPhil(1806)

Question 1209075: Find two nonnegative numbers whose sum is 9 and so that the
product of one number and the square of the other number is a
maximum.
Click here to see answer by ikleyn(52787)

Question 1209188: The first and last terms of an A.P are 1 and 121 respectively. Find
(a) the number of terms in the A.P
(b) the commons difference if the sum of its term is 671
Click here to see answer by math_tutor2020(3817)

Question 1198759: A products lift accelerates from rest to 0.16 m/s2
in 32 seconds. It then moves at constant velocity
for 33 seconds and then decelerates to rest in 15 seconds as . Lift pulley is 30cm
diameter carrying load 30 kg.
Apply dimensional analysis techniques and solve:
a) The linear velocity of the pulley.
b) The angular velocity of the cable.
c) The angular acceleration of the pulley.
d) The linear acceleration of cable.
e) The torque applied to the shaft.
State the formulae used to show that all values/units used are homogeneous. Given that :
v = vo + at , where , v ,is velocity , vo , is the initial velocity , a , is the acceleration and t is time.
Apply dimensional analysis techniques to develop two equations for power in terms of linear
velocity and angular velocity, from the formulae used above.
Click here to see answer by textot(100)

Question 1197649: A bank loan of $8000 is repaid in annual payments of $1000plus 10% interest on the unpaid balance.What is the total amount of interest paid?
Thank you.
Click here to see answer by ElectricPavlov(122)

Question 1209367: Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5 or 8.
Click here to see answer by mccravyedwin(407)

Question 1209367: Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5 or 8.
Click here to see answer by math_helper(2461)

Question 1209367: Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5 or 8.
Click here to see answer by greenestamps(13200)

Question 1209367: Find the sum of all positive integers less than 1000 ending in 3 or 4 or 5 or 8.
Click here to see answer by math_tutor2020(3817)

Question 1209366: In an arithmetic sequence, the 23rd term is 2, and the 38th term is 3. What is the 41st term?
Click here to see answer by greenestamps(13200)

Question 1209366: In an arithmetic sequence, the 23rd term is 2, and the 38th term is 3. What is the 41st term?
Click here to see answer by math_tutor2020(3817)

Question 1209366: In an arithmetic sequence, the 23rd term is 2, and the 38th term is 3. What is the 41st term?
Click here to see answer by ikleyn(52787)

Question 1209376: Laverne starts counting out loud by 5's. She starts with 2. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds 20, Shirley runs screaming from the room. What number does Laverne say that sends Shirley screaming and running?
Click here to see answer by mccravyedwin(407)

Question 1209374: When the same constant is added to the numbers a, b, and c, a three-term geometric sequence arises. If a = 60, b = 120, and c = 150, what is the common ratio of the resulting sequence?
Click here to see answer by htmentor(1343)

Question 1209373: A geometric sequence has 400 terms. The first term is 1600 and the common ratio is 9/10. How many terms of this sequence are greater than 1?
Click here to see answer by htmentor(1343)

Question 1209375: Let a_1, a_2, a_3, ..., a_8, a_9, a_{10} be an arithmetic sequence. If a_1 + a_3 + a_5 = 5 and a_2 + a_4 = -2, then find a_1.
Click here to see answer by ikleyn(52787)

Question 1209375: Let a_1, a_2, a_3, ..., a_8, a_9, a_{10} be an arithmetic sequence. If a_1 + a_3 + a_5 = 5 and a_2 + a_4 = -2, then find a_1.
Click here to see answer by math_tutor2020(3817)

Question 1209375: Let a_1, a_2, a_3, ..., a_8, a_9, a_{10} be an arithmetic sequence. If a_1 + a_3 + a_5 = 5 and a_2 + a_4 = -2, then find a_1.
Click here to see answer by greenestamps(13200)

Question 1209377: Find the sum of the following numbers.
1 2 3 4 ... 50
2 3 4 5 ... 51
3 4 5 6 ... 52
. . . . ... .
. . . . ... .
. . . . ... .
50 51 52 53 ... 99
Click here to see answer by Edwin McCravy(20056)

Question 1209378: What is the 1000th value of the following sequence?
1/1,1/2,2/2,1/3,2/3,3/3,1/4,2/4,3/4,4/4,...
Click here to see answer by Edwin McCravy(20056)

Question 1209378: What is the 1000th value of the following sequence?
1/1,1/2,2/2,1/3,2/3,3/3,1/4,2/4,3/4,4/4,...
Click here to see answer by mccravyedwin(407)

Question 1209388: Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is 2 greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator of the previous fraction by 1. He then multiplies all his fractions together. He has 3 fractions, and their product equals 10. What is the value of the first fraction he wrote?
Click here to see answer by greenestamps(13200)

Question 1209387: Let
a + ar + ar^2 + ar^3 + ...
be an infinite geometric series. The sum of the series is 3. The sum of the cubes of all the terms is 5. Find the common ratio.
Click here to see answer by greenestamps(13200)

Question 1209386: Evaluate the infinite geometric series
0.4 + 0.016 + ...
Express your answer as a fraction with integer numerator and denominator.
Click here to see answer by greenestamps(13200)

Question 1209385: Let a_1, a_2, a_3, ... be an arithmetic sequence. Let S_n denote the sum of the first n terms. If S_{10} = 1 and S_{200} = 1/2, then find S_{15}.
Click here to see answer by greenestamps(13200)

Question 1209400: Let a_1, a_2, a_3, \dots be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6.
Click here to see answer by math_tutor2020(3817)

Question 1209400: Let a_1, a_2, a_3, \dots be a sequence. If
a_n = a_{n - 1} + a_{n - 2}
for all n \ge 3, and a_{11} = 4 and a_{10} = 1, then find a_6.
Click here to see answer by greenestamps(13200)

Question 1186926: In order to ensure optimal health, a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.
Rather than order rabbit food that is custom-blended, it may be cheaper to order Rabbit-Gro and Lucky-Rabbit, and blend them for an optimal mix. Rabbit-Gro contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Lucky-Rabbit contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce.

Click here to see answer by CPhill(1959)

Question 1209590: Good evening find unknown numbers
21
49
76
224
467
514
1155
2683
5216
10544
26867
51510
95823
198669
357535
863317
1811764
3007503
5598802
14428676
33185509
54538862
111949941
227634408
400708894
1033162084
2102388551
3093472814
7137437912
14133072157
20112871792
42387769980
100251560595
146971536592
323724968937
1003651412950
1458252205147
2895374552463
7409811047825
15404761757071
19996463086597
51408670348612
119666659114170
191206974700443
409118905032525
611140496167764
2058769515153876
4216495639600700
6763683971478124
9974455244496707
30045390491869460
44218742292676575
138245758910846492
199976667976342049
525070384258266191
1135041350219496382
1425787542618654982
3908372542507822062
8993229949524469768
17799667357578236628
30568377312064202855
46346217550346335726
unknown
unknown
unknown
970436974005023690481
unknown
unknown
unknown
unknown
22538323240989823823367
unknown
unknown
unknown
unknown
1105520030589234487939456
unknown
unknown
unknown
unknown
21090315766411506144426920
unknown
unknown
unknown
unknown
868012190417726402719548863
unknown
unknown
unknown
unknown
25525831956644113617013748212
unknown
unknown
unknown
unknown
868221233689326498340379183142
unknown
unknown
unknown
unknown
29083230144918045706788529192435
unknown
unknown
unknown
unknown
1090246098153987172547740458951748
unknown
unknown
unknown
unknown
31464123230573852164273674364426950
unknown
unknown
unknown
unknown
919343500840980333540511050618764323
unknown
unknown
unknown
unknown
37650549717742544505774009877315221420
unknown
unknown
unknown
unknown
1103873984953507439627945351144005829577
Click here to see answer by greenestamps(13200)

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