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

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Question 923116: A rubber ball is dropped from a height of 9 meters. If it rebounds one-third of the previous fall approximately how far does it travel before it comes to rest?
Click here to see answer by srinivas.g(540)

Question 923193: -10, 20, -40, 80
Click here to see answer by MathLover1(20850)

Question 923276: Use the iterative rule to find the 12th term in the sequence.
an = �16 + 2n
a12 = _________
Click here to see answer by MathLover1(20850)

Question 923274: What is the common difference d of the sequence?
9, �8, �25, �42, �59, . . .
d = _________
Click here to see answer by Alan3354(69443)

Question 923710: What number comes next in 7,10,16,28 number sequence
Click here to see answer by Alan3354(69443)

Question 923713: What number comes next in 3,9,27,81 number sequence
Click here to see answer by Alan3354(69443)

Question 923713: What number comes next in 3,9,27,81 number sequence
Click here to see answer by TimothyLamb(4379)

Question 923797: Hi looking to figure out how to find the 83rd term, of arithmetic sequence with first term being 6 and common difference -1/2
Please help me,
Click here to see answer by Cromlix(4381)

Question 923746: If the time is 7:41pm &uadd41 minutes to tjst what would that equal
Click here to see answer by Alan3354(69443)

Question 923931: What number continues the following pattern: 3,-6,12,4,20,?
Click here to see answer by stanbon(75887)

Question 924172: what would the next 3 terms be for this sequence? 40,43,39,42,38,41,37
Click here to see answer by ewatrrr(24785)

Question 924170: what would the next 2 numbers be for this sequence? 5, 15, 35, 65, 105
Click here to see answer by ewatrrr(24785)

Question 924218: find the sum of the infinite geometric series a1=27 and r= -4/5
Click here to see answer by jim_thompson5910(35256)

Question 924343: Hello,
I have been recently working on a question (Maths Trick) but I cannot figure out how it works. I have used x as the number and tried to figure out the algebra but I cannot solve it. The trick is:
Think of a number, any positive integer
1. Square it.
2. Add the result to your original number.
3. Divide by your original number.
4. Add, oh, how about 17.
5. Subtract your original number.
6. Divide by 6.
The number you are thinking of now is 3!
Your help will be greatly appreciated in helping me to solve this Maths Trick.
Thanks again!

Click here to see answer by josgarithmetic(39618)

Question 924384: QUESTIONS: simplify the ratio of the following factorials
(n+2)! / n!
Click here to see answer by Theo(13342)

Question 924383: QUESTIONS : write down the nth term of each sequences as suggested by the pattern of the sequence. 1, 1/2, 3, 1/4, 5, 1/6, 7, 1/8...
please help me to find the solution.
Click here to see answer by Theo(13342)

Question 924391: Question : evaluate each of the following arithmetic series
1, -3, -7, ..., -75
Click here to see answer by wangsol(2)

Question 924501: f a,b,c and d are in H.P then ab+bc+cd equals
A)3ad
b)3ac
c)3bd
d)(a+b)(a-b)
Click here to see answer by MathLover1(20850)

Question 924562: -9 Common difference 1
Click here to see answer by Alan3354(69443)

Question 924657: The number of bacteria in milk doubles every 3 hours. If there are n bacteria at a given time, how many will there be at the end of 24 hours from then?
Click here to see answer by josgarithmetic(39618)

Question 924963: Find the sum of first 7 terms 4,12,36?

Click here to see answer by TimothyLamb(4379)

Question 924963: Find the sum of first 7 terms 4,12,36?

Click here to see answer by MathTherapy(10552)

Question 924540: 2x+y=12
x-y=3
Click here to see answer by Sam32399(5)

Question 925064: a n=1-n
Use the given formula to find the first three terms of each sequence. Thanks
Click here to see answer by MathLover1(20850)

Question 925265: Which is the 11th term in the sequence: 1/2,1,2,4,8...?
(Points : 1)
a. 256
b. 102
c. 1024
d. 512
Click here to see answer by ewatrrr(24785)

Question 925265: Which is the 11th term in the sequence: 1/2,1,2,4,8...?
(Points : 1)
a. 256
b. 102
c. 1024
d. 512
Click here to see answer by MathLover1(20850)

Question 925261: . Use the iterative rule to find the 6th term of the sequence.
an = 2 � 3n � 1
a6 = _________
Click here to see answer by MathLover1(20850)

Question 925261: . Use the iterative rule to find the 6th term of the sequence.
an = 2 � 3n � 1
a6 = _________
Click here to see answer by Edwin McCravy(20056)

Question 925275: Find the sum of A and B in the following pattern 0 , 3 , 8 , 15 , 24 , A , B

Click here to see answer by stanbon(75887)

Question 924749: 5) Find the value of S=(1/1!)+(3/2!)+(7/3!)+(13/4!)+(21/5!)+(31/6!)+(43/7!)+......
[Given that e^x = 1+(x/1!)+(x^2/2!)+.....]
A. 2e+2
B. 3e-2
C. 2e-1
D. 2e+1
Click here to see answer by Edwin McCravy(20056)

Question 925566: Insert 4 geometric means between 1/8 and 64.
I've worked on this so far:
an = a₁r^n � 1
a₁ = 1/8, a₆ = 64
64 = (1/8)r⁶⁻'
r⁵ = 512
r = 4
an = a₁r^n � 1
an = (1/8)(4)4^n � 1
and I don't know if I'm wrong or not, so please let me know if I am.
Click here to see answer by srinivas.g(540)

Question 925651: Which is the iterative rule for the sequence: 15.5, 13, 10.5, 8, 5.5, 3, �?
(Points : 1)
a. an = 15.5 − 2.5n
b. an = 18 � 2.5n
c. an = 15.5 + 2.5n
d. an = 18 + 2.5n
Click here to see answer by stanbon(75887)

Question 925649: What is the common difference d of the sequence?
�92, �74, �56, �38, �20, . . .
d = _________

Click here to see answer by MathLover1(20850)

Question 925648: Use the iterative rule to find the 7th term in the sequence.
an = 30 � 4n
a7 = _________

Click here to see answer by richard1234(7193)

Question 925652: . Which is the iterative rule for the sequence: 2, 9, 16, 23, 30, �?
(Points : 1)
a. an = �5 � 7n
b. an = 2 � 7n
c. an = 2 + 7n
d. an = �5 + 7n
Click here to see answer by MathLover1(20850)

Question 925762: Find the sum: 10 e 2i i=1.
Click here to see answer by Alan3354(69443)

Question 925863: 9 box equations where the number -5, -4, -3, -2, -1, 0 ,1, 2,3 used all rows, columns and diagonals add up to -3
Click here to see answer by Edwin McCravy(20056)

Question 926025: The function b = cs gives the total number of calories in a box of food that contains s servings, and each serving contains c calories.
Which function can be used to determine the number of calories in a box that contains 8 servings, given the number of calories per serving?
(Points : 1)
a. b(c) = 8c
b. b(c) = 8
c. b(s) = 8s
d. b(s) = 8
Click here to see answer by ewatrrr(24785)

Question 926024: The function s(m) = 5 + 4(m � 1) represents the number of stamps in Rudy�s stamp collection in month m.
What does the value 4 represent in this situation?
(Points : 1)
a. Rudy�s collection is worth $4.
b. Rudy collected stamps for 4 months.
c. Rudy began his collection with 4 stamps.
d. Rudy adds 4 more stamps to his collection every month.
Click here to see answer by ewatrrr(24785)

Question 926022: The function h(m) = 10 + 4m represents the height of a vine, in centimeters, m months after the vine was transplanted.
What does the value 10 represent in this situation?
(Points : 1)
a. The vine grew for 10 months.
b. The vine grows 10 cm each month.
c. The vine was 10 cm tall when it was transplanted.
d. The vine was 10 months old when it was transplanted.
Click here to see answer by rothauserc(4718)

Question 926023: The function c(p) = 6 � 2p � 1 represents the number of circles on page p in an artist�s book.
What does the value 6 represent in this situation?
(Points : 1)
a. There are 6 circles on the first page of the book.
b. There are a total of 6 pages in the book.
c. Every page contains 6 more circles than the previous page.
d. The number of circles on a page is 6 times the number of circles on the previous page.
Click here to see answer by rothauserc(4718)

Question 926020: Sequence : a,b,b,c,c,c,d,d,d,d.......
Find 250th term.
NOTE : please give a detailed solution with explanation of each step.
Click here to see answer by richard1234(7193)

Question 926106: what are the first four terms of 3n+1.

Click here to see answer by TimothyLamb(4379)

Question 926468: In the expansion of (x+y)n, the second term is 1620.the third term is 4320 and the fourth term is 5760,find the values of x,y and n
Click here to see answer by Edwin McCravy(20056)

Question 926339: Find the sum, if it converges.
1/3-1/9+1/27-...
Click here to see answer by Edwin McCravy(20056)

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