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

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Question 552039: If a ball rebounds three-fifths as far as it falls, how far will it (vertically) travel before coming to rest if dropped 14 feet?
Click here to see answer by Theo(13342)

Question 552544: I need some help with some homework. I'm struggling with these four problems:
1. What is the twenty-fifth term of the arithmetic sequence with a1 = �1 and d = �10?
2.What is the twenty-ninth term of arithmetic sequence with a1 = 13 and d = �5/2?
3. What are the two arithmetic means between �13 and 8?
4. What is Sn for the arithmetic series with d = �4, an = 27, and n = 9?
Thanks so much!
Click here to see answer by AnlytcPhil(1806)

Question 553542: A population of bacteria is growing according to the exponential model P=100e^70t, where P is the number of colonies and t is measured in hours. How many colonies are present initially?
A. 2.72
B. 70
C. 100
D. 1000
Click here to see answer by rapaljer(4671)

Question 553539: Which has the same value as (4+3i)^2
A. 7
B 7+24i
C. 25
D. 25 + 24i
Click here to see answer by rapaljer(4671)

Question 553548: Find the x-intercept of the function f(x)=a^x+1 - 1
A. (0,0)
B. (a, 0)
C. (-1, 0)
D. (a-1,0)
Click here to see answer by rapaljer(4671)

Question 553548: Find the x-intercept of the function f(x)=a^x+1 - 1
A. (0,0)
B. (a, 0)
C. (-1, 0)
D. (a-1,0)
Click here to see answer by stanbon(75887)

Question 553545: When Katie was born her mother invested $5000 in an account for her college savings. The interest rate is 3.5% compounded annually. To represent this, we can use the formula V = 5000(1+r)t where r represents the interest rate and t represents the time in years. How much will Katie have in her account when she turns 18?
A. 5,175
B. 7,127
C. 9,287
D. 12,472
Click here to see answer by stanbon(75887)

Question 554879: i need to find the nth term of a pattern with consecutive even numbers, ive tried many solutions but neither see to be working. please help.
Click here to see answer by KMST(5328)

Question 555043: 8x+2y+5z-3x+3z-3y=
Click here to see answer by edjones(8007)

Question 555329: What is the LCM of 84 and 138
Click here to see answer by jim_thompson5910(35256)

Question 555561: In a speed typing test, each girl found that the girl sit on the left type twice as much as she type. The teacher note that each girl type a whole numbe rof lines and all the girls typed 635 lines in total.
How many girl take the test?
Click here to see answer by KMST(5328)

Question 555763: V=lwh, for w

Click here to see answer by jim_thompson5910(35256)

Question 556845: help solve 72t^6/81t^10
Click here to see answer by stanbon(75887)

Question 557268: how to solve 33 7/12 + 45
Click here to see answer by bluemockingjay7(41)

Question 558170: I'm working with fraction exponents i.e. #roots. I know how to solve for the variable when it is an exponent, but this is a new lesson where I have to solve for the variable that is a base.

This what I've tried, but I've hit a dead end.
Problem:
Step 1: or is it
---I got same bases on both sides of the equation and had 4^(3-24) subsitute my value for 40, since (4^3)=64, but I would have to subtract 24 from either the exponent or from the whole side of the equation. Here's where I hit a wall and I don't know what to do after that since I tried to do both of my alternatives.
P.S. This is an excercise to get our feet wet for tomorrow's lesson.
Click here to see answer by KMST(5328)

Question 558346: The lengths of the three sides of a right triangle are given by three consecutive even integers. Find the lengths of the three sides.
Click here to see answer by Alan3354(69443)

Question 558345: The sum of the squares of two consecutive even integers is 1684. Find the two integers.
Click here to see answer by Alan3354(69443)

Question 558677: if the pattern 1 3 7 is contiued what would be the 5th term (1 3 7 ? ?)
Click here to see answer by unlockmath(1688)

Question 558751: What is the seventh term in this sequence
6,-18,54,-163...
Thank you for your help I am really stuck.
Click here to see answer by scott8148(6628)

Question 558856: 1/4,1/4,3/4,5/4
I tried to find the pattern but the two 1/4s got me please help
Click here to see answer by stanbon(75887)

Question 558951: Try to solve this sequence
112 , 2112 , 2122 ....
Calculate the further terms
Click here to see answer by Edwin McCravy(20056)

Question 559241: cube root of 44.5
Click here to see answer by rfer(16322)

Question 559371: what's next 5 numbers in this sequence? 1, 6, 12, 17, 34, 39, 78...
Click here to see answer by KMST(5328)

Question 559630: what would the 7th pattern be to the following sequence: 1, 1+4=5, 1+4+9=14
Click here to see answer by solver91311(24713)

Question 559368: what's next in this sequence? 1, 6, 12, 17, 34, 39, 78...
Click here to see answer by richard1234(7193)

Question 560377: what is the next number in the arithmetic sequence 3, 11, 19, 29
Click here to see answer by kkasko(46)

Question 561862: The sum of 40 consecutive integers is 100 what is the largest integer

Click here to see answer by Edwin McCravy(20056)

Question 562209: What is the arithmetic sequence of 1, 1/4, 1/9, 1/16?
Click here to see answer by richard1234(7193)

Question 562232: What is the common difference in the arithmetic sequence of 1, 1/4, 1/9, 1/16?
Click here to see answer by richard1234(7193)

Question 562803: What is the nth term for this pattern?....... 2,8,18,32,50
Click here to see answer by scott8148(6628)

Question 562803: What is the nth term for this pattern?....... 2,8,18,32,50
Click here to see answer by issacodegard(60)

Question 563150: How can we show if the sequence αn = 2cos(nπ) is monotone or not?
Click here to see answer by richard1234(7193)

Question 563669: Are the sets equal? {4, 4, 11, 11, 17} = {4, 11, 17}
Click here to see answer by jim_thompson5910(35256)

Question 563844: find the missing number, n, in data set
28,n,2,19, and 28
mean = 19
Click here to see answer by prateekagrawal(56)

Question 564340: I need to know the formula for adding whole numbers (1+2+3+4...) to get a sum over 1000. I know the answer is 45 but I need the formula to figure it out.

Click here to see answer by ad_alta(240)

Question 565548: find the sum of the first 30 terms of 4+7+10+13+16+19....
Click here to see answer by htmentor(1343)

Question 565635: Which number should come next at the end of this series: 1/12, 1/6, 1/3, 2/3?
Possible answers: 3/4, 4/3, 3/2
Click here to see answer by ad_alta(240)

Question 565988: write the first three terms of an arithmetic sequence if the fourth term is 10 and d=-3
Click here to see answer by Tatiana_Stebko(1539)

Question 566014: S10=-20 and d=4 find a1

Click here to see answer by stanbon(75887)

Question 566162: The question is: what is the sum of 4+11+18+....+4001
I have been taught to add the first and last number, so i get 4005. Then I usually divide by half of the last number, which would be 2000.5
However, I know this only works if the numbers go up by one, not seven. This is where I get lost.
Click here to see answer by richard1234(7193)

Question 566625: Given the sequence 1331, 1000, 729, x, y, z, 125, . . . , what is the sum of x, y, z? Please show me the steps.
Click here to see answer by richard1234(7193)

Question 567485: A combination lock for a bicycle contains four digits, each of which can have a value of 0, 1, 2, 3 or 4. How many different sequences of numbers can open this lock? I came up with 120 digit combination.
Click here to see answer by scott8148(6628)

Question 567777: Suppose that the sum of two whole numbers is 20, and the sum of their reciprocals is 5/16. Find the numbers.
Click here to see answer by stanbon(75887)

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