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 6533: Please help me solve
Click here to see answer by longjonsilver(2297)

Question 6523: What is the fourth term of (x + y)^6 ?
Click here to see answer by Mike(39)

Question 6532: Please help me answer the following question: If y varies inversely as x and y=8 when x=4, find y when x=16
Click here to see answer by Mike(39)

Question 6531: Please help me solve ln (x - 4) < 6
Click here to see answer by Mike(39)

Question 6529: Please help me solve

Click here to see answer by Mike(39)

Question 6528: How do I find the standard deviation to the nearest tenth of the following set of data? {47, 61, 93, 22, 82, 22, 37}
Click here to see answer by Mike(39)

Question 6535: What describes the number and type of roots of the equation 4x^3 - 6x^2 + 15x + 2= 0?
Click here to see answer by khwang(438)

Question 6616:
hi
i want to ask that how can i find the sum of the equations like
1*+2*+......+n* where * = 2

Click here to see answer by khwang(438)

Question 6524: Where is the center of 25(x+5)^2 + 4(y-3)^2 = 100 ?
Click here to see answer by rapaljer(4671)

Question 7015: the 12th term of an arithmatic series is 42 and the sum of the first 17 terms is 51. find the common difference of the series and the first three terms.
Click here to see answer by longjonsilver(2297)

Question 8958: Identify the fifth term in the sequence in which a1= 243 and r=-1/3
Click here to see answer by longjonsilver(2297)

Question 9413: I have a question. I know the answer is 14, but I don't know how to put in in an equation to show how I came up with the answer.
I am a two-digit number. when I am multiplied by the sum of my digits, the result is 70. What number am I?
Click here to see answer by prince_abubu(198)

Question 9414: I have 5oo bills. some of them are $1.00, some are $100.00, and some are $500.00. When we are added together our result is $50,000.00. How many of each bills do I have.
Click here to see answer by rapaljer(4671)

Question 9823: Find the exact fraction value foe the number 0.123123123....... using series only.
Click here to see answer by longjonsilver(2297)

Question 10386: what is the next 2 terms?
9, 3, 1, 1/3, __, __
Click here to see answer by thecampusnerd(13)

Question 10615: find the sum of first n natural numbers
Click here to see answer by longjonsilver(2297)

Question 10923: 2.4=-A+(-5.1)
Click here to see answer by rapaljer(4671)

Question 16682: b + 2 = 27 + 2b/ 3

Click here to see answer by elima(1433)

Question 21447: If 2 numbers have a product of 75, a quotient of 3, and a difference of 10, what's the sum of these 2 numbers?
Click here to see answer by venugopalramana(3286)

Question 22136: find the sum of the geometric series.
14 - 7 + 7/2 - 7/4 + ...
Click here to see answer by longjonsilver(2297)

Question 22134: form a sequence that has two arithmetic means between -2 and 58.
Click here to see answer by venugopalramana(3286)

Question 21580: could you please help me with this problem
Divide:

Click here to see answer by venugopalramana(3286)

Question 23368: Please help me on this problem. I will write it how it looks in my text book.The two jugs stood side by side on the shelf. One contained a solution that was 60% antiseptic, and the other contained a solution that was 90% antiseptic. How much of each should be used to get 50 milliliters of a solution that is 78% antiseptic?
Click here to see answer by Paul(988)

Question 23417: Find the first five (5) terms of the sequence (begin with n = 1).
A=n!/n^2
I still do not understand how to do this one.
Click here to see answer by rapaljer(4671)

Question 23417: Find the first five (5) terms of the sequence (begin with n = 1).
A=n!/n^2
I still do not understand how to do this one.
Click here to see answer by stanbon(75887)

Question 23805: FInd the sum of each infinte geomertric series if it exists.
10 + 1 + 0.1 + 0.01 +...

And can you please tell me how to did it. I am struggling with it.
Click here to see answer by Paul(988)

Question 25006: in a circle i have 8 numbers, a mystery number then 173, 268, 934, 252, 520, 89, and 311. What is the mystery number?
Click here to see answer by AnlytcPhil(1806)

Question 25545: Ok, this is one that has baffled not only myself but my parents and boyfriend as well. This is a problem that no one seems to be able to figure out. Do you think you could help me?
A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter's life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said," If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies." As he'd been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
How much money would Mr. Brown have to put on the 32nd square?
How much would the traveling salesman receive if the checkerboard only had 32 squares?
Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How much money would the farmer need to give the salesman?
Click here to see answer by venugopalramana(3286)

Question 25541: I have an assignment due on arithmetic series of numbers. I have been studying my book and can't seem to figure out what I am supposed to do to make or solve the equations. Is there anyway you can help? Thank you in advance.
Use the arithmetic series of numbers 1,3,5,7,9,...to find the following:
What is d, the difference between any 2 numbers?
Using the formula for the nth term of an arithmetic series, what is 101st term?
Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
What observation can you make about these sums of this series(HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3 etc.)?
I know it seems like a lot but it really is just one problem broken down into several sections. I have no idea how to so this so I would be VERY thankful for any help you can give me.
Click here to see answer by askmemath(368)

Question 25943: What is the geometric notation for a parallel lie?
Click here to see answer by Earlsdon(6294)

Question 26238: I am very frustrated. I am working on geometric series of numbers and thought that it would be easy but, I have not done this in a while and I have to admit that I am perplexed. Here is what I must solve:
Use the geometric series of numbers 1, 2, 4, 8,...to find the following:
a) What is r, the ratio between 2 consecutive terms?
(I got r=1)
b) Using the formula for the nth term of a geometric series, what it the 24th term?
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Could you please help refresh my memory by showing me step by step how to complete this first set of problems? Thank you!!!!

Click here to see answer by stanbon(75887)

Question 27288: Use the formula for an arithmetic series to find each sum.
40+42+44+...+68.
Thank you very much
Click here to see answer by sdmmadam@yahoo.com(530)

Question 26650: 1) Identify the fifth term in the sequence in which a^2=40 and r=1/2
2) Find the sum of the geometric series in which a^1=125,r=2/5, and n=4
Click here to see answer by venugopalramana(3286)

Question 27325: what number less than 3000 when divided by 10 has a remainder of 9 and when divided by 9 has a remainder of 8 and when divided by 8 has a remainder of 7 and when divided by 7 has a remiander of 6 and when divided by 6 has a remainder of 5 and when divided by 5 has a remainder of 4 when divided by 4 has a reaminder of 3 when divided by 3 has a remainder of 2 and when divided by 2 has a remainder of 1 and when divided by has a remainder of 0
Click here to see answer by venugopalramana(3286)

Question 28030: find the mean, median, and mode of the set: 1,2,2,3,3,3,4,4,4,4
Click here to see answer by venugopalramana(3286)

Question 29695: 3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following.
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms?

c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms?

d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?

Click here to see answer by sdmmadam@yahoo.com(530)

Question 29783: 1)Use the arithmetic sequence of numbers 2, 4, 6, 8, 10� to find the following:
a)What is d, the difference between any 2 terms?
Answer:
Show work in this space.

b)Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.

c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Show work in this space.

d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Show work in this space.

e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?
Answer:
Click here to see answer by venugopalramana(3286)

Question 29589: I am having trouble with this problem, could you please help me.
3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27… to find the following.

PROBLEMS:
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms?

c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms?

d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Thank you in advance for all your help.
Click here to see answer by sdmmadam@yahoo.com(530)

Question 30045: The value of square-root(2/pi) * Integral(e to the power -square(t)/2 ),
where "t" is a variable from 4 to infinity is equal to what?
Click here to see answer by AnlytcPhil(1806)

Question 30508: I'm looking to find th 52nd term of the following harmonic series.
1+ 1/5 + 1/9 + 1/13 + 1/17 +...
Click here to see answer by checkley71(8403)

Question 30511: What is the arithmetic mean of the numbers 5 and 3125?
Click here to see answer by checkley71(8403)

Question 30509: What is the geometric mean of the numbers 5 and 3125?
Click here to see answer by sdmmadam@yahoo.com(530)

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