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 1091993: What is d value of the following sequence?
5/4, 1/2, (whole fraction is negative) -1/4, -1, (Whole fraction is negative)-7/4.
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Question 1091988: Find the three arithmetic means between 12 and -16.
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Question 1091987: Find the six arithmetic means between 1 and 29.
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Question 1091991: If t1 = 4 and tn = tn-1 + (the whole fraction is neagtive) -5/2 find the first 4 terms of the sequence.

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Question 1091989: Find the 3rd term of an arithmetic sequence with t2 =9/2 and t5 = 6.

A. 5

B. 4

C. 3

D. 2

Click here to see answer by MathLover1(20850)

Question 1092011: A sequence has the pattern described by 70+25n. When does the value exceed 1000 for the first time? Assume n starts at zero.
Click here to see answer by josmiceli(19441)

Question 1092033: The third term of an AP is 45 and the 23 term term is 315. find the 59th term.
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Question 1092041: tn=2n-5
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Question 1092010: Write the first five numbers in the sequence described by the expression 4-3n. Assume n starts at zero.
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Question 1092090: Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 3 + 3 + 9 + ... + 81
Can you please explain so I get it, because i know how to write this in the simple way, i just get really confused when it comes to using sigma and everything..
Click here to see answer by Fombitz(32388)

Question 1092083: Can someone help me? Thank you.
When superballs sprang upon the scene in the 1960s, kids across the US were amazed that these hard rubber balls could bounce to 90% of the height from which they were dropped. If a superball is dropped from a height of 2m, how far does it travel until it stops bouncing?
How can I set up? Is it finite or infinite geometric series?

Click here to see answer by Fombitz(32388)

Question 1092175: Determine whether the sequence converges or diverges. If it converges, give the limit.
108, -18, 3, -1/2 ...

Please help me fast , I need the answer super fast! Also could you please explain the answer.
Click here to see answer by Fombitz(32388)

Question 1092202: The sum of the first two terms of a geometric series is 90. The third term is 24.
A. Show That there are two possible series and find the term and the common ration in each case.
B. Show that both series converge and find their respective sums.
Click here to see answer by greenestamps(13200)

Question 1092222: if a15 = 20, a30 = -13 then what is r, S50 (Geometric Sequence)
Click here to see answer by Theo(13342)

Question 1092221: if S10 = 50, S50 = then what is a10, S100 (Geometric Sequence)

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Question 1092220: if SS2 = 10, S10 = 2 then what is a1, d (Arithmetic Sequence)
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Question 1092232: Seve is training for a long distance walk. He walks for 10 km in the first week, then
each week thereafter he walks an additional 500 m. If he continues this pattern for
a year, how far does he walk:
a in the last week
b in total?
Click here to see answer by Boreal(15235)

Question 1092224: A tennis ball is dropped from a height of 40m and bounces in place. Each time
it strikes the ground, it bounces to 40% of its previous height. Find the total
vertical distance traveled by the ball if it is stopped immediately on the 10th
time it hits the ground.
Click here to see answer by Boreal(15235)

Question 1092219: if S10 = 50, S50 = 0 then what is a10, S100 (Arithmetic Sequence)
Click here to see answer by greenestamps(13200)

Question 1092279: The sum of the first two terms of an arithmetic progression is 23. The sum of
the last two terms is -25. Find the sum of the progression if its first term is 13.
Click here to see answer by greenestamps(13200)

Question 1092278: if S2 = 10, S10 = 2 then what is a1, d (Arithmetic Sequence)
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Question 1092277: if S10 = 50, S50 = 0 then what is a10, S100 (Geometric Sequence)
Click here to see answer by greenestamps(13200)

Question 1092307: Find a_n for the arithmetic series
with S₁₆ = -288, and a₁ = -21
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Question 1092307: Find a_n for the arithmetic series
with S₁₆ = -288, and a₁ = -21
Click here to see answer by Edwin McCravy(20056)

Question 1092302: The Sum of first 20th terms is 200 and Sum of next 10 terms is 400.What is the 40th term?
Click here to see answer by greenestamps(13200)

Question 1092380: A finite arithmetic sequence has 12 terms. The last term is 100 and the common difference is 3.What is the firt term

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Question 1092380: A finite arithmetic sequence has 12 terms. The last term is 100 and the common difference is 3.What is the firt term

Click here to see answer by greenestamps(13200)

Question 1092408: What is the next number 0,1,4,12,29
Click here to see answer by Alan3354(69443)

Question 1092410: Please help... Thank you.
Determine whether the sequence converges or diverges. If it converge, give the limit. U 1=1 and U n+1=(Un)/(3) for n≥1
I got U2=1/3, U3=1/9, U4=1/27, but not sure about converge.
Click here to see answer by Boreal(15235)

Question 1092409: Can someone help? Thank you.
Write the sum using summation notation, assuming the suggested pattern continues.
1+8+27+...+(n+1)^3
I solved like this: ∑(k+1)^3 (top of sigma sign: n, bottom of sigma sign: k=0). I could not write it properly here...
Please fix this if I am wrong.

Click here to see answer by Edwin McCravy(20056)

Question 1092371: The first difference of a sequence is the arithmetic sequence 3, 5, 7, 9, 11, ...... Find the first six terms of the original sequence in each of the following cases.
A. The first term in the original sequence is 3.
B. The sum of the first two terms in the original sequence is 11.
C. The fifth term in the original is 40.
Click here to see answer by greenestamps(13200)

Question 1092428: How do I determine whether the sequence converge or diverges. If it converges, give the limit.
U1=1, U n+1= Un/3 for n≥1 (1,n+1, n after U should be smaller size).
Please help. Thank you.
Click here to see answer by Theo(13342)

Question 1092499: Find the sum of sequence
35+36+37+38+...+128
Click here to see answer by ikleyn(52788)

Question 1092625: No wind energy "farms" use large wind turbines to generate electricity from the wind. At a typical installation, a single modern turbine can produce an average power about 200 kilowatts. (This average takes wind variations into account.) How much energy, in kilowatt-hours, can such turbine generate in a year? Given that the average household uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by a single wind turbine?
Click here to see answer by Alan3354(69443)

Question 1092661: Hi there , I am getting a little struggle with sequence can you please answer this question. ,72,18,4.5 and $3.90, ,$4.00,$4.05 also the last one
$4.50,$4.75, ,$5.25.

Click here to see answer by richwmiller(17219)

Question 1092845: Find an expression for the nth term of the sequence:
-2, 0, -2, 0....
Click here to see answer by Edwin McCravy(20056)

Question 1092849: How do i find the sequences -5, 3, -2, 1, -1, 0 and 1, 5, 14, 30, 55
Click here to see answer by greenestamps(13200)

Question 1092849: How do i find the sequences -5, 3, -2, 1, -1, 0 and 1, 5, 14, 30, 55
Click here to see answer by Edwin McCravy(20056)

Question 1092890: 12,13,15,19,27,43 what is the next number

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Question 1092926: Please help. What kind of sequence is this? 2,-9/11, 14/101, -19/1001...
Thank you.
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Question 1092938: Show the sequence defined by tn=4n+7 is an ap

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Question 1092952: Can you help? Is there a sequence neither a geometric nor an arithmetic?
There is a sequence problem, and I need to write an explicit form for it. But it does not apply to regular geometric or arithmetic formula. So I had to make one.
Is it ok? Thank you.
Click here to see answer by Theo(13342)

Question 1092948: (-1/2+3/4)+5/6. How to do the steps to get the answer. Please show me the steps
Click here to see answer by josmiceli(19441)

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