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 1140429: Find the square root of 1+√3
Click here to see answer by greenestamps(13200)

Question 1140439: Given the sequence:2;5;8;......
(1) write down the next two terms.
(2) Prove that none of the terms of this sequence are perfect squares.
Hello everyone can I please get help on this question plz help
Click here to see answer by ikleyn(52787)

Question 1140444: Consider the sequence of numbers : 2;5;2;9;2;13;2;17;.....
Calculate the sum of the first 100 terms of the sequence
Please help me I begg.
Click here to see answer by Boreal(15235)

Question 1140519: 1,-1,3 what is the next three term of
arithmetic sequence

Click here to see answer by josgarithmetic(39617)

Question 1140552: find the 9th term of the geometric sequence 57,61,65

Click here to see answer by ikleyn(52787)

Question 1140593: Find three numbers in arithmetic progression whose sum and product are six and six respectively
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Question 1140594: The sum of the first three terms of an AP is twenty four and the sum of there square is two hundred twenty four.find first three terms of AP
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Question 1140634: 1;3;5 are the first three terms of the first differences of a quadratic sequence
The 7th term of the quadratic sequence is 35
(1) Determine the 6th and 5th terms of the quadratic sequence
(2)Determine the nth term of the quadratic sequence
Help please I was revising and I got this Q
Click here to see answer by greenestamps(13200)

Question 1140627: Consider the arithmetic series
3+7+11+15+19+23+27+......and answer the questions that follow
a(i) T1 and S1
(ii) Express T1 interms of S1
b(i) T2 and S1
(ii)Express T2 interms of S2 and S1
Please can someone help me with this question I begg

Click here to see answer by ikleyn(52787)

Question 1140686: _ , -10 , _ , _ , _ , 14
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Question 1140687: In an AP consisting of 15 terms, the sum of the last five terms is 305. If the sixth term is 26, find the sum of this AP
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Question 1140702: t is an even number in the series 1/t + 3/t + 5/t +.......+ t-1/t
(1) Determine the number of terms in the series in terms of t.
(Determine the sum of the series in terms of t.
(3) Hence or otherwise evaluate :
(1/4 + 3/4) + (1/6 + 3/6 + 5/6) + (1/8 + 3/8 + 5/8 +7/8)+.....+ (1/50 + 3/50 + 5/50)+....+(49/50)
Can I get help please
Click here to see answer by greenestamps(13200)

Question 1140769: (1) Prove that in any arithmetic series of which the first term is a and where the constant difference is d,the sum of the n terms is given by Sn=n/2[2.a+(n-1)d]
Please can get help with this Q
Click here to see answer by ikleyn(52787)

Question 1140819: GRAPHICAL ANALYSIS OF DATA
1. The list below shows the ages of the first 20 fans to arrive at a professional basketball game.
38, 39, 14, 46, 9, 25, 27, 33, 60, 11, 14, 37, 25, 28, 16, 30, 42, 35, 35, 47
Part A: Display the fan age data on this stem-and-leaf plot. (1 point)

Part B: Use your plot from Part A to display the data in this frequency table. (1 point)

Part C: Use your table from Part B to display the data on this histogram. (1 point)

Part D: Use your results from Parts A - C to answer these questions. (6 points)
What does it mean that the fan data are numerical and univariate?

Are the data discrete or continuous? Explain.

Which age group had the most fans? Explain how to find the answer using each of the three data displays.

Write a question that can be answered using the stem-and-leaf plot but cannot be answered using the frequency table or histogram.

MEASURE AND DESCRIBE DATA
2. Jason is the captain of his basketball team. The list below shows how many points Jason scored in each of the first 10 games of the season.
18, 23, 14, 26, 16, 10, 12, 24, 14, 13
Part A: Find the range, mean, median, and mode of Jason's scores. Show your work. (4 points)

Part B: Use your mean result from Part A to find the variance and standard deviation of Jason's scores. Show your work. Round your answers to the nearest hundredth. (2 points)

Part C: Are your results in Part B for a sample or a population? Explain. (1 point)

Part D: Use your results from Parts A - C to describe the shape of the distribution of Jason's scores. (1 point)

Part E: Use your results from Parts A - D to answer these questions. (3 points)
If Jason scored 40 points on his next game, would it be an outlier for his first 11 games? Explain.
How would a score of 40 affect the range, mean, median, and mode of Jason's scored points?

If Jason could add 10 points to the number of points he scored each game, how would it affect the mean, median, and standard deviation of his scored points?

If Jason could double every game's scored points, how would it affect the mean, median, and standard deviation of his scored points?

RANDOM VARIABLES
3. The table below shows the probabilities of rolling sums from 2 to 12 with a pair of 6-sided dice. Use the table to find the mean of the random variable x (the expected value of the sum rolled with 2 dice).
x
2
3
4
5
6
7
8
9
10
11
12
P(x)

Part A: Complete the table below. You do not need to reduce fractions. The first row is filled in for you. (5 points)
i
xi
P(xi)
xiP(xi)
1
2
1/36
2/36
2
3
2/36

3
4
3/36

4
5
4/36

5
6
5/36

6
7
6/36

7
8
5/36

8
9
4/36

9
10
3/36

10
11
2/36

11
12
1/36

Part B: Find the mean of the random variable x. Use this formula: .(3 points)

EXPERIMENTAL DESIGN
4. Below is a list of 30 students numbered from 00 to 29. Use the random number table below to put exactly 6 of these students into a treatment group. Start with the first line of the table (line 101). List the students of the treatment group in the order in which their numbers come up in the table.
00 Aaron
01 Buffy
02 Chandler
03 Cindy
04 Drusilla
05 Eric
06 Fallon
07 Graham
08 Heather
09 Hsin-Chi
10 Ismail
11 Jasmine
12 Kiefer
13 Lucia
14 Monte
15 Naomi
16 Otis
17 Polly
18 Quincy
19 Rachael
20 Sarah
21 Stacy
22 Tasha
23 Turan
24 Ukiah
25 Valerie
26 Wahib
27 Xandra
28 Yale
29 Zach
Part A: Search through the list for pairs that match student numbers and circle each one found. If a student number is repeated, only use the first occurrence. Stop when you have 6 matches. (3 points)

Part B: List the 6 matching student numbers you found. (3 points)

Part C: Which 6 students will be in the treatment group? (3 points)

REPORTS and EXPERIMENTS
5. Devon wants to know if drinking milk before bed helps teenagers sleep. He chooses 10 friends on his high school basketball team for his study. Every night for one month, the friends drink a glass of milk before bed and later record how many hours they slept that night.

Part A: Describe three reasons why Devon's study design is flawed. (3 points)

Part B: After one month, Devon finds that his 10 friends slept an average of 0.5 hour more each night when they drank milk before bed. Based on this, Devon concludes that drinking milk makes teenagers sleepy. What is one reason why Devon's conclusion is most likely invalid? (1 point)

Part C: A study conducted by a major milk manufacturer showed that 83% of American teenagers prefer drinking milk to drinking soda. What are two reasons why this statistic cannot be trusted? (2 points)

6. A lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. He has 100 mice available. He randomly assigns 50 of them into each group. He trains the first group to run the maze at 9:00 am and trains the second group to run the maze at 9:00 pm. Each mouse is trained the same way and the last three run times are recorded.
Part A: Describe what is being measured in this experiment and what variable is being manipulated. (1 point)

Part B: Control, randomization, and replication are ways to design an experiment so that bias is reduced. Describe whether or not this experiment incorporates each of these principles into the experimental design. (6 points)
Control

Randomization

Replication

Click here to see answer by ikleyn(52787)

Question 1140842: Consider the following general term for a sequence
a^n=13+(n+11)−6
find the first five terms of the sequence and its common difference? Is it an arithmetic sequence or not?
Click here to see answer by ikleyn(52787)

Question 1140859: a, a + 4, a + 8, . . .
Write the nth term in terms of the first term of sequence.
(Thank you 😭)
Click here to see answer by ikleyn(52787)

Question 1140894: Mr John deposited $80 at the beginning of the year 2000 and $20 thereafter, find the amount it will be accumulate at the end of year 2008
Click here to see answer by ikleyn(52787)

Question 1140958: which term of the arithmetic sequences: 3x - 4 ; 4x - 3; 7x - 6 ;.....is equals to 5x + 4
Click here to see answer by ikleyn(52787)

Question 1141039: Find the common ratio of the geometric sequence with a first term -7 and a sixth term -1701.

Click here to see answer by Edwin McCravy(20056)

Question 1141053: For what values of x will (..., x+1, x+5, 3x+2, ...) be a geometric sequence?
Click here to see answer by Edwin McCravy(20056)

Question 1137739: Prove by induction that for all positive integers value of n:
is an integer multiple of 9.
Click here to see answer by Edwin McCravy(20056)

Question 1141091: what is the pattern rule between 5 to 46

Click here to see answer by josgarithmetic(39617)

Question 1141127: If a, b, c, and d are in G. P., Then show that (a+b)², (b+c)² and (c+d)² are also in G. P
Click here to see answer by greenestamps(13200)

Question 1141173: Find the sum of the first 12 terms of arithmetic sequence with a common difference of -5 if its 23rd term is 556.
Click here to see answer by josgarithmetic(39617)

Question 1141237: next number in the following sets of series
3,-6,12,4,20,?
7,16,8,27,9,?
2,7,26,101,400,?
7,21,8,72,9?
Click here to see answer by greenestamps(13200)

Question 1141237: next number in the following sets of series
3,-6,12,4,20,?
7,16,8,27,9,?
2,7,26,101,400,?
7,21,8,72,9?
Click here to see answer by Alan3354(69443)

Question 1141231: please help me with this mathematical induction 1/2^1+1/2^2+1/2^3+....+1/2^n =1-1/2^n.
Click here to see answer by math_helper(2461)

Question 1141229: please help me with prove of mathematical induction of this question 1+r+r^2+r^3+....+r^n =1-r^n+1÷1-r.
Click here to see answer by math_helper(2461)

Question 1141342: Find the common difference d for this sequence. 7,3,-1,-5,-9
Find a formula in simplest form, for the nth term a sub n for the sequence
So, I know that the common difference is -4 but I do not know the formula.
Click here to see answer by josgarithmetic(39617)

Question 1141346: The fourth term of an arithmetic sequence is 17, and the sixth term is 11. Find the second term.
Click here to see answer by josgarithmetic(39617)

Question 1141346: The fourth term of an arithmetic sequence is 17, and the sixth term is 11. Find the second term.
Click here to see answer by greenestamps(13200)

Question 1141349: What is the missing term of the geometric sequence {45,_,1620}?
Click here to see answer by Edwin McCravy(20056)

Question 1141362: Hello! I’m really stumped on this. The question says to consider the infinite geometric series:
sigma infinity n=1 -4(1/3)^n-1
and it says the lower limit of the summation notation is “n=1”. It then says to write the first four terms of the series, asks if the series diverge or converge, and if the series has a sum, find it. I think the series converge, and if I solved for the sum correctly, I got -5.9..., but I can’t figure out the first four terms right. Can you help? And have I solved the rest correctly?
Click here to see answer by math_helper(2461)

Question 1141414: if boy is coded as ylb then uncode nmz

Click here to see answer by greenestamps(13200)

Question 1141414: if boy is coded as ylb then uncode nmz

Click here to see answer by josgarithmetic(39617)

Question 1141476: Please help me solve this
Use the Binomial Theorem to expand (x-3y)^5
Click here to see answer by greenestamps(13200)

Question 1141476: Please help me solve this
Use the Binomial Theorem to expand (x-3y)^5
Click here to see answer by MathLover1(20850)

Question 1141470: what comes next in the sequence 135,3231,23634,828549,??
Click here to see answer by Alan3354(69443)

Question 1141509: Please help me solve this:
Find the fifth term in the expansion of (ab-1) ^20. Use the term formula.
Click here to see answer by Alan3354(69443)

Question 1141509: Please help me solve this:
Find the fifth term in the expansion of (ab-1) ^20. Use the term formula.
Click here to see answer by ikleyn(52787)

Question 1141509: Please help me solve this:
Find the fifth term in the expansion of (ab-1) ^20. Use the term formula.
Click here to see answer by MathTherapy(10552)

Question 1141510: Find the term containing y^3 in the expansion of (root 2 +y)^12
Root 2 is square root of 2.
Please help me solve
Click here to see answer by Alan3354(69443)

Question 1141530: 1,-8,27,-64,125
Click here to see answer by ikleyn(52787)

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