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 1072393: What are next 4 terms of -1,2,12,40?
Click here to see answer by rothauserc(4718)

Question 1072584: Find the sum.
1 + 3 + 5 + ... + 1153
Click here to see answer by ikleyn(52788)

Question 1072565: find the 8th terms of the following series;
6.500 , 9.750 , 14.625
calculate rounding to the third decimal place, and show your workings
Click here to see answer by KMST(5328)

Question 1072745: 2;5;8 prove that none of the terms of this sequence are perfect square
Click here to see answer by ikleyn(52788)

Question 1072777: One sequence of alternating terms of the series 1+2+3+4+5+8+... forms an arithmetic progression, while the other sequence of alternating terms forms a geometric progression. Sum the first 10 terms of each progression and hence find the sum of the first 20 terms of the series.
Click here to see answer by ikleyn(52788)

Question 1072648: First question: Three numbers re in a arithmetic sequence and their sum is 21 if the first number is increase by 1 second by 3 and the third by 10 the new numbers are in a arithmetic sequence. Find the possible value of the original
Second question: the sum of the first twenty term of the following sequence is 1680 2exponent x + 2 exponent x -1 + 3 2 exponent x +....
Use the formula to calculate the value of x.
Third question: the sum of first and second term of a converge series is 30. The sum of all term is 54 determine the common ratio r, with r>0 and the first term.
Fourth question: the sequence Tn=(n-1) raise to 2 -8 is given.. 1: calculate the first term three terms of the sequence.. 2: which term of the sequence will be more than 56

Click here to see answer by ikleyn(52788)

Question 1072844: what is the number sequence or pattern for 0, 1, 8, 27, 64 ....
Click here to see answer by rothauserc(4718)

Question 1072844: what is the number sequence or pattern for 0, 1, 8, 27, 64 ....
Click here to see answer by MathTherapy(10552)

Question 1072878: 4. The value of a lathe originally valued at �3000 depreciates 15% per annum. Calculate its value after 4 years. The machine is sold when its value is less than �550. After how many years is the lathe sold?
Click here to see answer by Edwin McCravy(20056)

Question 1072952: given a1=28 an=-77 and sn =-196 in an A.P find the
10th term and the sum of the first 10 terms
Click here to see answer by Edwin McCravy(20056)

Question 1072881: If the population of Great Britain is 55 million and is decreasing at 2.4% per annum, what will be the population in 5 years� time?
Click here to see answer by Alan3354(69443)

Question 1072975: 4,12,7,21,16,?
Click here to see answer by ikleyn(52788)

Question 1073001: Write an explicit formula for the Nth term of the arithmetic sequence 101,95,89,83,...
Click here to see answer by ikleyn(52788)

Question 1072876: The purchase value of an ofﬁce computer is $12,500. Its annual depreciation is $1875. Find the value of the computer after 6 years.
Click here to see answer by Fombitz(32388)

Question 1073061: What is third number among following list
32, 29, 65
Click here to see answer by ikleyn(52788)

Question 1073135: Given that , and are consecutive terms of an arithmetric progression, prove that x, y and z are consecutive terms of a geometric progression
Click here to see answer by KMST(5328)

Question 1073224: What is the sum of 1275309178427
Click here to see answer by Alan3354(69443)

Question 1073261: Find the sum of first 20 term of the series 1+1+2�2+1+2+3�3+1+2+3+4�4....
Click here to see answer by Edwin McCravy(20056)

Question 1073367: How many terms are there between 100 and 200 of an arithmetic
sequence 7n+5 ?

Click here to see answer by Edwin McCravy(20056)

Question 1073396: The first two terms in a sequence are a and b. The third term in the sequence is the sum of the previous two terms. The fourth term is the sum of the second and third terms. These sums give you the sequence a, b, a + b, a + 2b. Using this pattern, which of the following expressions is the sixth term in the sequence?
I am really not sure but this is how I started to work it out. Thank you look forward to your reply.
a,b
a+b =step 3
a + 2b = step 4
2b + a = step 5

Click here to see answer by ikleyn(52788)

Question 1073521: If �Hose A� can fill a barrel in 2 minutes and �Hose B� can fill a barrel in 4
minutes, how many minutes will it take both hoses together to fill the barrel.
Click here to see answer by josgarithmetic(39618)

Question 1073523: If �Hose A� can fill a barrel in 2 minutes and �Hose B� can fill a barrel in 4
minutes, how many minutes will it take both hoses together to fill the barrel.
Click here to see answer by josgarithmetic(39618)

Question 1073520: . Write the following into an algebraic expression and simplify completely.
The perimeter of a rectangle with length 4x-1 and width 3x+2

Click here to see answer by ikleyn(52788)

Question 1073583: how many terms are there in the progession 11,18,25,32, _ _ _ _ _ ,676?

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Question 1073594: The 5th and 10th term of AP are 23 and 48 respectively.find its 18th term?
Click here to see answer by Fombitz(32388)

Question 1073626: what is the sequence of -4,8,-12,16?
Click here to see answer by ikleyn(52788)

Question 1073587: The ﬁrst and second terms of a geometric progression are cos θ and sin θ respectively.
(a) Find the common ration r and the third term of this geometric progression in terms of θ.
(b) Given that the ﬁrst and third terms of this geometric progression and tan θ are three consecutive terms of an arithmetic progression, ﬁnd the general solution for θ. Give your answer in radians correct to two decimal places.
(c) Suppose that 0 < r < 1. Find the sum to inﬁnity of the geometric progression in this case.
Click here to see answer by KMST(5328)

Question 1073751: What are the three next terms in the sequence, 1, 1, 2, 3, 5
Click here to see answer by htmentor(1343)

Question 1073751: What are the three next terms in the sequence, 1, 1, 2, 3, 5
Click here to see answer by ikleyn(52788)

Question 1073746: 1 4 7 10
Click here to see answer by Fombitz(32388)

Question 1073859: A catapult launches its ammo across a battlefield. The Height of the rock launched at
any time after it has been �fired� can be found using the equation h(t)=48t-16t^2
determine how long itll take the rock to reach 36 feet
Click here to see answer by josmiceli(19441)

Question 1073866: A geometric series has 8 terms whose sum of the first three terms is 13/9 and the sum of the last three terms is 351. Find the first term and the common ratio of the series
Click here to see answer by KMST(5328)

Question 1073879: a super-bouncy ball rebounds half the height it drops. the ball is dropped from a height of 176 feet. How far off the ground is the ball when it has travled a total of 500 feet?

Click here to see answer by rothauserc(4718)

Question 1073856: Good morning,
It is about a series of colored hexagons. The numbered of colored hexagons are:
1,6, X , 54.
The question is what is the "X".
I found (pure guess) that it is 24., but could not find the logical reason.
Can you help please.
Thank you
Click here to see answer by Fombitz(32388)

Question 1074025: What is the first term of the geometric sequence presented in the table below?

n 5 7
an 176 704

Click here to see answer by ikleyn(52788)

Question 1074129: Calculate the first ten term of an arithmetic progression whose 5th term is 24 and the difference between the 7th and 10th term is 15
Click here to see answer by Edwin McCravy(20056)

Question 1074139: 588 14 680
679 20 569
790 64 699
360 91 290
226 0.9 900
235 0.7 250
450 96 169
400 46 790
246 24 220
160 74 130
880 67 449
156 23 580
338 48 170
148 33 247
169 62 570
134 89 126
579 17 458

239 48 350
557 70 299
369 85 780
450 99 234
249 55 690
367 60 235
145 0.4 590
557 79 388
349 69 135
368 78 459
159 5? ???

Click here to see answer by ikleyn(52788)

Question 1074078: If (3-x), 6, (7-5x) are consecutive terms of a geometric progression with constant ratio r>0 find x and constant ratio
Click here to see answer by htmentor(1343)

Question 1074275: the 6th term is 50 and the 11th term is 85 find the 21st term
Click here to see answer by ikleyn(52788)

Question 1074390: If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 4133.

Click here to see answer by ikleyn(52788)

Question 1074451: What is the function rule for -8,-11,-14,-17,-20,-23
Click here to see answer by Fombitz(32388)

Question 1074512: the common difference 1500, 2700, 4860, and 8748
or the common ratio of 1500, 2700, 4860, and 8748.
Click here to see answer by Alan3354(69443)

Question 1074719: 3, -6, 12, 4, 20, ?
Click here to see answer by KMST(5328)

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