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 421049: Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.
-14,-10,-6,-2, so on

Click here to see answer by rfer(16322)

Question 421052: What is the geometric sequence for 1, 1/3,1/9,1/27
Click here to see answer by rfer(16322)

Question 421187: what is y=1/2(8x-1^2)-3/2
Click here to see answer by MathLover1(20850)

Question 421258: THREE NUMBERS IN ARITHMETIC PROGRESSION HAVE THE SUM OF 33 AND PRODUCT OF 1232. FIND THE THREE NUMBERS.
Click here to see answer by dnanos(83)

Question 421300: What is the next two number of this sequence?
13 6 11 9 9 12 7 _ _
Click here to see answer by sudhanshu_kmr(1152)

Question 421473: 1,3,9,27,... what sequence is this?
Click here to see answer by robertb(5830)

Question 421854: the sum of 3 nos is 24 among them 1number is equal to half of the sum of other 2 nos but four times the difference of them find the numbers
Click here to see answer by mananth(16946)

Question 421965: In the sequence below, describe the pattern AND give the next 2 terms.
2, 12, 72, 432, _____, ______

Click here to see answer by MathLover1(20850)

Question 422194: Find the common difference, the first term, and the general formula if the 7th term is 25 and the 21st term is 81.
I'm assuming the formula used is an = a1 + (n-1)d, but I'm not sure how to find a1 or d. Please help!
Click here to see answer by stanbon(75887)

Question 422243: How to find the sum of sigma with the formula being 3an -n, and the starting and ending points being one and five, respectively?
I approached the problem by setting the formula equal to zero and solving for an, which gives me an = -n/3, ultimately getting a sum of -5.
Is this right at all or am I way off?
Thank you so much.
Click here to see answer by stanbon(75887)

Question 422370: please give me 3 examples of problem solving using arithmetic sequence with solution ...
Click here to see answer by stanbon(75887)

Question 422414: The sum of a finite geometric sequence for n terms with common ratio r and initial term a1 is:
s(n)=a1 (1-r^n/1-r)
Find the sum of the first 10 terms of 4, 2, 1, 1/2, 1/4
I am EXTREMELY stuck and don't know where to even begin! All help is greatly appreciated! thanks!
Click here to see answer by solver91311(24713)

Question 423792: for the sequence {2,4,8,16...} write an expression for the nth term of the sequence
Click here to see answer by Gogonati(855)

Question 424600: An infinite geometric series has common ratio r. The sum to infinity of the series is four times the first term.
Show that r = 0.75
Click here to see answer by richard1234(7193)

Question 424575: Predict the general term, or nth term, for the sequence: 1, square root 3, square root 5, square root 7, 3...
I know that the answer equation is An= 1r^n-1 but I can't figure out what the r term would be.
Click here to see answer by richard1234(7193)

Question 425758: Hello,can anyone help me with these series and sequences questions? I have a test on them tomorrow and I'm struggling with these questions about Arithmetic Progression:
1. The 5th and 11th terms of Arithmetic Progression are 7 and 61 respectively. Find the common difference and the 1st term.
2. The 1st term of a Arithmetic Progression is -3 and the 15th term is 53. Find the common difference.
3. The sum of the 7th and 9th terms of an Arithmetic Progression is 52 and the sum of the 5th and 16th terms 67. Find the 1st term and the common difference.
Thank you!
Click here to see answer by stanbon(75887)

Question 425762: a)How do I find the arithmetic mean of:
i) 9 and 21
ii) 6+sqrt(3) and 6-sqrt(3)
b) Insert 5 arithmetic means between 11 and 71.
Thank you very much for your assistance!
Click here to see answer by stanbon(75887)

Question 426107: two jars of the same jam are sold at different prices, number one: �1.59 for 454g and number 2: �1.25 for 340g. which one is better value for money?
Click here to see answer by ewatrrr(24785)

Question 426144: The second term of a geometric series is 24 and the fifth term is 3
a) show that the common ratio of the series is a half
b) Find the first term of the series
C) Find the sum to infinity of the series
Click here to see answer by ewatrrr(24785)

Question 426687: what would be the answer to this?
Write a rule for each sequence.
1, -1/3, 1/9, -1/27, ....

30,0-10, 10-3, -10/9, ....
6, 12, 24, 48, ...
50, 25, 12.5, 6.25, ....
Click here to see answer by ewatrrr(24785)

Question 426816: what is the ninth term when the first term is 4 and the common ratio is -6?

Click here to see answer by stanbon(75887)

Question 426920: 1) How do I write down the 6th term of the sequence in which Tn=4n-7?
2) Is -356 a member of the sequence Tn=4-5n?
Hello, I am having trouble with these two problems on series and sequences. Thank you for your assistance. :)
Click here to see answer by www.mathmartian.com(5)

Question 426974: suppose you estimate the area under a curve using inscribed rectangles and then estimate the area using circumscribed rectangles. how will the two estimates for the area compare?
Click here to see answer by robertb(5830)

Question 426924: Hi, can anyone help me with these two questions on series and sequences?:
1) For the sequence 15,12,9,... find the common difference and the nth term.
2) If 3x-1, 2x+2 and 2x-1 are in Arithmetic Progression, find value of x.
Thank you for your time and consideration!
Click here to see answer by Gogonati(855)

Question 427260: if x-1/x=2 ,then x8+1/x8=?

Click here to see answer by richard1234(7193)

Question 427328: find the sum of the multiples of 3 from 3 to 99 inclusive
Click here to see answer by Theo(13342)

Question 427328: find the sum of the multiples of 3 from 3 to 99 inclusive
Click here to see answer by Edwin McCravy(20056)

Question 427529: sequence problem
What is the third # in the following pattern?
2, 10, ?, 250, 1250
I've tried multiplying by five to get 50, but the game, "My Sims Agent" says this is not the correct answer!
Will you please help?
Thank you,
Drew

Click here to see answer by richard1234(7193)

Question 427617: how to determine if the number 5240365220553 is a square number
Click here to see answer by Alan3354(69443)

Question 428166: What represents the series 1+ 1/3+ 1/9+ 1/27+ 1/81+ 1/243 using sigma notation?
Click here to see answer by htmentor(1343)

Question 428621: Write a variable expression to describe the rule for each sequence. Then find the hundredth term.
1. 3, 6, 9, 12, ...
i am really really really really really really confused. please help??
Click here to see answer by stanbon(75887)

Question 428946: I need some direction on how to start this sequence. I understand that a sequence is an ordered list. Would this be when I use a1, a2, a3 and so on?
Rain forests are defined as forests
that grow in regions that receive more than 70
inches of rain each year. The world is losing an estimated
49 million acres of rain forests annually. Give
symbolic, numerical, and graphical representations
for a sequence that models the total number of acres
(in millions) lost over a 7-year period

Click here to see answer by stanbon(75887)

Question 429008: Hello, can anyone assist me with these two questions on series and sequences? I am very frustrated:
1) Is 207 a member of the sequence 3,7,11,...?
2) Find the first term of the sequence -7,-5,-3,... which is greater than 400.
Thank you very much!
Click here to see answer by richard1234(7193)

Question 429014: Hi, my son and I are having trouble figuring out his homework on "series and sequences". I don't know about you but I have never heard of that. Anyway these are the three problems:
1. Find the sum of the 1st 20 terms of the sequence 7,13,19...
2. Write the sum of the 1st n terms of the sequence -5,-2,1,...
3. How many terms of the sequence -19,-15,-11,... must be taken to give a sum of 98?
Thank you for your time and consideration! Your help is greatly appreciated.
Click here to see answer by richard1234(7193)

Question 429011: How do I insert 5 arithmetic means between 11 and 71?
Click here to see answer by robertb(5830)

Question 429208: Consider the sequence 8, 6, 3, �1, �6, ...

a. Find the next two terms of the sequence.
b. Write an explicit formula for the sequence.
c. Write a recursive formula for the sequence.
I did parts a and c and understand them, but I can't figure out how to write the explicit formula. I would really appreciate some help.
Click here to see answer by stanbon(75887)

Question 429250: write the missing two numbers in the pattern and explain how you got your answer. 4, 24, 144, __, __, 31, 104
Click here to see answer by poliphob3.14(115)

Question 429173: Consider the sequence 8, 6, 3, �1, �6, ...
a. Find the next two terms of the sequence.
b. Write an explicit formula for the sequence.
c. Write a recursive formula for the sequence.
I got part a, but I'm not sure how to do the other two parts, considering that the sequence in neither arithmetic or geometric.
Click here to see answer by htmentor(1343)

Question 429511: Can someone show me how to work these?
Find the 5th term for each:
1: A1=20, An=1/2A(n-1)+2
2: An=8n-5
3: A1=1/2, An=2A(n-1)
I came up with 35 for #2, but I'm not even sure that's right. These are confusing me!
Thanks!
Click here to see answer by vleith(2983)

Question 429783: What is the 2000th term of the following sequence 8,11,16,23
Click here to see answer by robertb(5830)

Question 430428: The 4th term of an arithmetic sequence is 16.The 8th term is four times the 1st term.
(a)find the general term T(n)of the sequence.
(b)Find the smallest term which is greater than 500.
Click here to see answer by robertb(5830)

Question 430417: 140% of what number is 35?
Click here to see answer by robertb(5830)

Question 430761: hi i have to find out the value of the greatest element in the range of this relation with these numbers.
(0,0), (1,5), (2,8), (3,9), (4,8), (5,5), (6,0)
thank you sooo much
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