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

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Question 1084070: A collection of chairs is set up into 22 rows. The first row has
96 chairs, and each row after that one has 2 less chairs than the
preceding row. How many total chairs are there in the collection?
Click here to see answer by Edwin McCravy(20056)

Question 1084122: the third term of an A.P is 16 and its 6th term is 34 .find a:the common difference b:the first term c:the 20th term d:the sum of the first and 20 terms

Click here to see answer by ikleyn(52787)

Question 1084171: Please give the recursive formula in both subscript and function.
2,-6,18,-54
Click here to see answer by jim_thompson5910(35256)

Question 1084210: Evaluate the sum:
4/sigma/n=1 (2/3)^n-1
Click here to see answer by jim_thompson5910(35256)

Question 1084203: Find p so that p+7, 3p+9, p+3,... form an arithmetic sequence
Click here to see answer by ikleyn(52787)

Question 1084169: Common radio of the following GP and the number of terms 10/7,1.�...343/1000
Click here to see answer by stanbon(75887)

Question 1084214: pattern:1/2;2/5;6/8;8/11
write down the next two terms of the
pattern and determine the general term
Click here to see answer by Edwin McCravy(20056)

Question 1084273: The Scrabble tournament is designed such that the losers of each round are eliminated from the next round. The winners continue to play until a final match determines the champion. If there are 512 entries in the tournament, what is the total number of matches that will be played in this tournament?
Click here to see answer by ikleyn(52787)

Question 1084284: how much space would you leave between the house and the first stone?
Click here to see answer by Alan3354(69443)

Question 1084388: Each year, the value of a car depreciates to 70% of the value from the previous year.
A car was bought new for $67000. What is the value of the car after 7 years?
Click here to see answer by Alan3354(69443)

Question 1084385: A store will take 10% off the cost of an item each week until the item is sold.
Determine the cost of a $375 item 9 weeks from now
Click here to see answer by Alan3354(69443)

Question 1084386: Caitlyn is back for the summer after completing her 1st year at Queen's University.
She's been offered two jobs that will keep her busy during the 4 months (17 weeks)
that she's in town. The 1st job pays $325/month with a monthly raise of $100, and
the 2nd job pays $50/week with a weekly raise of $10. Which job will yield Caitlyn
the higher pay and by how much?
Click here to see answer by jorel1380(3719)

Question 1084522: Find the sum of all of the 3-digit positive integers.
Click here to see answer by htmentor(1343)

Question 1084522: Find the sum of all of the 3-digit positive integers.
Click here to see answer by Alan3354(69443)

Question 1084526: 1 0 -2 -6 ? Solve this
Click here to see answer by rothauserc(4718)

Question 1084552: The sum to m term of the series 1 +11+111...... upto m term is equal to:
Click here to see answer by math_helper(2461)

Question 1084676: the 7th term of an AP is 19 and the 8th term is 22.find the sum of the first 40th terms of the series
Click here to see answer by Boreal(15235)

Question 1084729: 1+5+9+ ... +49+53
Click here to see answer by jorel1380(3719)

Question 1084777: what is the deriving rule of -5,-2,1,4
Click here to see answer by Edwin McCravy(20056)

Question 1084780: what is the deriving rule of -5,-2,1,4?
Click here to see answer by josmiceli(19441)

Question 1084776: what is the rule of -5,-2,1,4
Click here to see answer by josgarithmetic(39617)

Question 1084758: What must be the value of k so that 5k-3,k-2,and 3k-11 will form an arithmetic sequence?
Click here to see answer by josgarithmetic(39617)

Question 1084810: Find the first term and the common difference of an arithmetic sequence if its 5th term is 33 and the 20th is 123

Click here to see answer by Edwin McCravy(20056)

Question 1084924: How can I find the value of m if 6-2m, 2m+1 and 5m form an arithmetic sequence?
Click here to see answer by Theo(13342)

Question 1084924: How can I find the value of m if 6-2m, 2m+1 and 5m form an arithmetic sequence?
Click here to see answer by MathTherapy(10552)

Question 1085009:
I need the answer for question (i) and (ii) both of them please: (2) Let {a_n} and {b_n} for n = 1,2,3,... . (i) The sequence {a_n} satisfies the following relation: . Express the general term a_n in terms of n when a₁ = (ii) The general term of {b_n} is given by Prove that

Click here to see answer by Edwin McCravy(20056)

Question 1084905: 1+1=1
1+1=13
1+1=49
1+1=94
Click here to see answer by ikleyn(52787)

Question 1085161: -1,3,7,11
Click here to see answer by josgarithmetic(39617)

Question 1085159: 128 / 5
Click here to see answer by Alan3354(69443)

Question 1085157: find the nth term for the sequence 7,10,13,16
Click here to see answer by math_helper(2461)

Question 1085157: find the nth term for the sequence 7,10,13,16
Click here to see answer by ikleyn(52787)

Question 1085157: find the nth term for the sequence 7,10,13,16
Click here to see answer by MathTherapy(10552)

Question 1085216: For the sequence 1,6,20,56,..., what is a_n?
Click here to see answer by AnlytcPhil(1806)

Question 1085203: What is the nth term of
A.0 2 6 12 20
B.-4 -2 2 5 8
C. 8 11 14 17 20
Click here to see answer by emathwiz(15)

Question 1085243: 1+1=1 1+1=13 1+1=49 1+1=94 What is the dependency/relation between each one of them ? If it doesnt make any sense try 1+1=1! 1+1=13! 1+1=49! 1+1=94!

Click here to see answer by ikleyn(52787)

Question 1085246: Insert seven arithmetic means between 3 and 23.
Click here to see answer by AnlytcPhil(1806)

Question 1085264: On an expedition to seize his enemy's elephants, a king marched two yojanas the first day. Say,intelligent calculator, with what increasing rate of daily march did he proceed, since he reached his foe'scity, a distance of eighty yojanas, in a week?

Click here to see answer by josmiceli(19441)

Question 1085308: given a 1=4 find the 7th term of the recursive sequence using: an=2an-1 -3, for n_>2
Click here to see answer by ikleyn(52787)

Question 1085307: -1, 1/4, -1/7, 1/10, -1/13,...
Click here to see answer by ikleyn(52787)

Question 1085313: Find the first five terms of the sequence given the following recursive formula: a1=8, and an=10-3an-1, for n_>2
Click here to see answer by jim_thompson5910(35256)

Question 1085312: Find the next two terms of the following sequence: 13,4,-11,-32,...
Click here to see answer by addingup(3677)

Question 1085040: Hello, I am kind of stumped at how I need to approach this problem. I'm fairly sure that you have to use sequences to solve this, but I am unsure of how to write it down to even begin to solve it. I hope this isn't too confusing to read, but it's the only way I can type it out. I appreciate any time and effort that you put into this to solve it.
Thanks in advance for your help!

Anthony is an astrobiologist studying a spherical alien organism that replicates itself when exposed to dihydrogen monoxide. The initial organism has a radius of 4 Mum (a Mum is one-millionth of a meter).
When exposed, it grows 4 similar copies of itself, tangent to and equally 1 spaced around the parent organism, but with only 1/ 4 the radius.
As the exposure continues, each member of the successive generations grows 4 additional copies of itself, each with 1/4 the radius of the prior generation.
This growth, diagrammed below, will continue for as long as exposure continues.
Table------------------------
Generation / New spheres / New Surface Area Added / New Volume Addded
1 ------------------------ 1 ------------------------ 64pi ------------------------ 256pi/3
2 ------------------------ 4 ------------------------ 16pi ------------------------ 16pi/3
3
4
n
30. Find the combined surface area of all the organisms as n tends to infinity, if possible.
31. Find the combined volume of all the organisms as n tends to infinity, if possible. Recall that for a sphere with radius r, the surface area SA = 4pir^2, and the volume = 4.3pir^2
Click here to see answer by Theo(13342)

Question 1085334: what is the geometric sequence of -2,_,_,-16,-32,-64
Click here to see answer by josgarithmetic(39617)

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