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 853892: sixth term of an AP. Is 37 and tenth term 53 and fine
the common difference
Click here to see answer by ewatrrr(24785)

Question 853885: What is the formula for this Fractional Progression?
72/65, 100/75, 132/85, 168/95, 208/105, ...
Click here to see answer by richwmiller(17219)

Question 853882: What is the formula for this Fractional Progression?
56/33, 80/39, 140/51, 176/57, 260/69 ...
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Question 853876: Find the first term and the common difference of the arithmetic sequence whose 5th term is 7 and 13th term is 39. Can you please help?
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Question 854063: how many terms must be added in an arithmetic sequence whose first term is 11 and whose common difference is 3 to obtain a sum of 1092

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Question 854204: Use the addition problems below to answer the question.
Based on this pattern, what is the sum of
1/2+1/4+1/8+1/16+...+1/1024?
Click here to see answer by richwmiller(17219)

Question 854204: Use the addition problems below to answer the question.
Based on this pattern, what is the sum of
1/2+1/4+1/8+1/16+...+1/1024?
Click here to see answer by aditya2117(32)

Question 854209: There are four numbers in an Arithmetic Progression. The sum of the two extremes is 8, and the product of the middle two numbers is 15. What are the numbers?

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Question 854100: Ok so I have a sequence of 3,7,15... I need to know the sum of 100 terms in this sequence how would I go about doing so?
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Question 853975: Which number comes next 35 15 7 79 40
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Question 854262: what is the next random number 42 17 61 31 49
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Question 850726: Hi,
Is there a general closed form formula for finding an expansion expression of the following "formal" finite product?
(1+x^(a1)*z)(1+x^(a2)*z).......(1+x^(an)*z)
Where, all exponent a1 through an is a random natural number.
I am looking for a nice compact formula like Cauchy product formula as seen in G. Chrystal Algebra part II, 316ff.
Thanks
Charles

Click here to see answer by richwmiller(17219)

Question 845402: I am looking for a mathematical formula (equation) for the following scenario:
A challenge is played by X number of participants.
Each participant contributes the same number of Y points to the challenge (when they join).
Thus, the total points in the challenge at any given time is: X*Y points.
The points ares distributed according to the following rule (for which I need a formula):
1. The person in 1st place, takes 50% of the points.
2. For the remaining (X-1) participants, the remaining points are distributed in a descending order of value.
e.g. Challenge A has 10 participants and each participant puts in 10,000 points. With total points in the challenge being 100,000 points.
Person in the 1st place gets - 50,000 points
The remaining 9 participants get the remaining 50,000 points distributed in a decreasing order of value
For example (one such scenario):
#2 - 12,000
#3 - 10,000
#4 - 9,000
#5 - 8,000
#6 - 5,000
#7 - 3,000
#8 - 2,000
#9 - 1,000
Can this be modeled mathematically?
Thank you.

Click here to see answer by richwmiller(17219)

Question 854332: 1/tan 60 ,sin 90, tan 60,...
form a sequence.
calculate the fourth term
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Question 854332: 1/tan 60 ,sin 90, tan 60,...
form a sequence.
calculate the fourth term
Click here to see answer by Vladdroid(91)

Question 850848: The patterns array problem
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
17 18 19 20 21 22 23 24 25
What patterns can be found in the array? Explain you thinking in responding to the following questions. Do not just provide an answer.
a. What is the first term of the nth row? The last term of the nth row?

b. What is the sum of ALL the terms in the first n rows?

c. What is the total number of terms in the first n rows?
Click here to see answer by richwmiller(17219)

Question 848824: what number is 2nd in the series four, 40 and fourteen?
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Question 854375: witch term of the arithmetic sequence 6,11,16.....186
Click here to see answer by ewatrrr(24785)

Question 843809: (Please help me with this question?)
The sum of two numbers is 3. Four times the larger number plus three times the smaller number is 25. Find the numbers.
The larger number is___?
and the smaller number is___?
Click here to see answer by richwmiller(17219)

Question 854472: How do I change a mixed number percent into a fraction? I need to find the fraction for 53 1/8%.
Bonnie
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Question 854472: How do I change a mixed number percent into a fraction? I need to find the fraction for 53 1/8%.
Bonnie
Click here to see answer by ewatrrr(24785)

Question 854458: What is the nth term of the arithmetic sequence?
7, 5, 3, 1, �
A.
�2n
B.
7 � 2n
C.
9 � 2n
D.
n � 2
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Question 843349: How to solve An=7n+11. Solving for the third term
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Question 845914: Find smallest number when it is divided by 7,9 and 11 with remainder is 1, 2 and 3 respectively.
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Question 845914: Find smallest number when it is divided by 7,9 and 11 with remainder is 1, 2 and 3 respectively.
Click here to see answer by Alan3354(69443)

Question 854530: What are the missing terms of the geometric sequence -3, _, _, -375?
A)-127, -251
B) 127, 251
C)15, 75
D) -15, -75
Click here to see answer by DrBeeee(684)

Question 854532: What are the missing terms of the arithmetic sequence
-8, _, _, 3?
A)-10/3, -1/3
B)-13/3, -2/3
C)-5, 0
D)-4, 1
Click here to see answer by richwmiller(17219)

Question 854541: What are the two arithmetic means between -13 and 8?
A)-3, 4
B)-4, 3
C)-6, 1
D-5, 2
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Question 854537: What are the two geometric terms between 2 and 1/4?
A)17/12, 5/6
B)1, 0
C) 1, 1/2
D)5/4, 1/2
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Question 854515: Find two arithmetic means between 17 and 29
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Question 854574: Algebra 2
Find the pattern: -1, 2, -3, 4, -5, 6
Thanks!
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Question 854628: For arithmetic sequence 14,__,__,__,2
It tells me to
find d
Find 23
Find a n in simplest form
Click here to see answer by stanbon(75887)

Question 854678: a and b represent 2 different whole numbers .If A + B = 216 and A - B = 38 , find the value of B
Click here to see answer by Fombitz(32388)

Question 854755: when n=18 the value of 3n-11 is
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Question 842985: The sum of 16 terms of an A.P is -504 while the sum of the 9 terms is -126.
Find the sum of 30 terms.

Click here to see answer by richwmiller(17219)

Question 854793: Given the functions f(n)=500 and g(n)= (9/10)^n-1, combine them to create a geometric sequence, an, and solve for the 11th term
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Question 854813: Find Out the value for blank space.
8,12,21,__,62,98
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Question 855000: The sum of the first 25 terms of an arithmetic series with a common difference of 5 is 1300. Find the first term of the series.
Click here to see answer by stanbon(75887)

Question 855046: What is Sn of the geometric series with a1=4, an=256, and n=4?
A)84
B) 336
C) 340
D)260
Click here to see answer by richwmiller(17219)

Question 855038: What is the twenty-ninth term of arithmetic sequence with a1=13 and d=-5/2?
A)-62
B)83
C) 88
D) -57

Click here to see answer by richwmiller(17219)

Question 855041: What is the twenty-fifth term of the arithmetic sequence with a1=-1 and d=-10?
A) -240
B) -250
C) -251
D) -241
Click here to see answer by richwmiller(17219)

Question 855044: What is Sn of the geometric series with a1=-81, r=-2/3, and n=5?
A)26
B) -39
C) -55
D)211
Click here to see answer by richwmiller(17219)

Question 854996: How you can find an arithmetic sequence that is related to the sequence of perfect cubes, 1, 8, 27, 64,125,...?
Click here to see answer by KMST(5328)

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