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

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Question 742937: Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is, find the common difference. (Assume n begins with 1.)

My teacher does more simplified versions of these problems so when we are given ones such as these I get confused as to how to go about them. Some explanations would be greatly appreciated as well as a quick answer to this.
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Question 742986: The first 5 numbers in a sequence are 5,6,8,11 and 15. What are the 8th and 10th numbers in the sequence?
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Question 743009: List the first four terms of the sequence defined by an =(n + 1)!/2n for for n is greater than or equal to 1.
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Question 743007: The sequence an is defined recursively by the rules a0 = 0, a1 = 3, and for n is greater than or equal to 2,an = an-1 - an-2. What is the value of a4??
Click here to see answer by davethejackal(28)

Question 743058: Write an equation for the nth term of the given arithmetic sequence.

7, 13, 19, 25
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Question 743334: Some sequences involve a pattern but are not arithmetic. Find the sum of the first 72-terms in the sequence 6,8,2,..., where An=(A(n-1))-(A(n-2))(The last term ia equal to the (last term minus 1) minus (the last term minus 2))
So, An is the last term in the sequence n= the total terms in the sequence (72)
Thank you
Click here to see answer by Edwin McCravy(20056)

Question 743327: Find the indicated 25th partial sum of the arithmetic sequence.
A_#1=100, A_#25=220, n=25
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Question 743400: The sum of all terms of the arithmetic progression having ten terms except for the first term is 99 and except for the sixth term 89. Find the third term of the progression if the sum of the first term and the fifth term is equal to 10.
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Question 743379: A furniture manufacturer makes wooden tables and chairs. The production process involves two types of labor: carpentry and finishing. A table requires 2 hours of carpentry and 1 hour of finishing, and a chair requires 3 hours of carpentry and 1/2 hour of finishing. The profit is $35 per table and $20 per chair. The manufacturer's employees can supply a maximum of 108 hours of carpentry work and 20 hours of finishing work per day. How many tables and chairs should be made each day to maximize the profit?
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Question 743687: 3 numbers add to 27 and multiply together to make 288. These numbers also fall into an arithmetic sequence. Show your work.
With the use of guess and check, I have found the answers to be 2, 9, and 16. They add to 27, multiply to 288, and are in an arithmetic sequence. I don't know how to solve this algebraically, however, especially within the series and sequence unit. Any help would be apreciated, thanks.
Click here to see answer by Edwin McCravy(20056)

Question 734289: If 111 equals 13 and 112 equals 24 and 113 equals 35 and 114 equals 46 and 115 equals 57, then what does 117 equal?
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Question 743862: How do you find the sum of 7+10+13+..........+100 ???
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Question 744368: In an arithmetic series s6 = 162 and t6 = 47. What is the common difference for the terms in this series?
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Question 744441: Hello, this isn't an arithmetic sequence question, but a geometric one. I need to find the rate of the following geometric sequence,
9 (nine), 3√3 (three square root of 3),3(three),... and the next three terms of the sequence. How can I do it?
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Question 744581: The fourth and eighth terms in a geometric sequence are 144 and 9 respectively, what are the first three terms in the sequence?
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Question 744462: Find the first 5 terms of the sequence an=2n^2-8
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Question 744647: Solve for x :
2x/3 + 1/4 = x/3 - 1/12
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Question 744798: I need to find the partial sum of 1+5+9+...+109
I understand how to find partial sum. I just haven't been able to figure out the common difference between the numbers.
So far, I have the equation set up as 109=1+(n-1)d
I just need to find d.
Could you explain to me how to find this answer?
Click here to see answer by MathTherapy(10552)

Question 744976: Find A1 and d for an arithmetic sequence with these terms:
A4 = 9
A7 = 18
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Question 745012: help with geometric how to get the answer and steps
1- 1/2+1/4-1/8+1/16
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Question 745077: Please help If the number of terms of an Arithmetic sequence is 15 and the value of it's middle term is 10 then find the sum of it's terms is there any rule that i can solve it with?? Thanks
Click here to see answer by sachi(548)

Question 745093: Arithmetic progression
If a1;d and sum is known, is it possible to get n?
Thank you
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Question 745099: Find the general term an for the geometric sequence
a1= -5, a2= 10

an=
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Question 745099: Find the general term an for the geometric sequence
a1= -5, a2= 10

an=
Click here to see answer by sachi(548)

Question 745180: When given t2=4 and t5=22, how would you find t23 in a arithmetic sequence?
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Question 745330: What is the sum of all the integers between the square root of 19 and the square root of 77?
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Question 745185: what is the equation for the sequence 16, 14, 11, 7, 2...
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Question 745541: Find the twentieth term of the arithmetic sequence with a1 = 15 and d = 4.
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Question 745856: for the sequence,describe the pattern, write the next term, and write a rule for the nth term
1,2,4,8
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Question 746174: Please help me solve : ((4x^2-x-12)/(x^2+9x+18)) / ((x^2+x-20)/(x^2+8x+15))
Your awesome
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Question 746281: If the third term and fifth term of a geometric progression are 225 and 5625 respectively, determine the sixth term.
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Question 746463: A fireplace contains 46 bricks along its bottom row. If each row above decreases by 4 bricks, how many bricks are on the 12th row?
Determine if this is an geometric or arithmetic series or geometric or arithmetic sequence.
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Question 746518: what integer would come next in the following pattern 18,3,-12
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Question 746682: Evaluate the determinant of the matrix.
0 -4
-6 -2

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Question 746694: Identify the slope of the line y = -x � 3
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Question 746784: the sum of three numbers is 9 and their product is 24;find them
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Question 746908: the ratio between sue and her brother sam is 3:7 if sam is 145 cm tall how tall is sue..

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Question 747121: Please help me solve this problem, this is my first time seeing it and i dont understand. "What is the 15th term in the sequence using the given formula Cn=3n-1"
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Question 746572: 81,108,144
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Question 746679: Perform the indicated operation. Find (f-g)(4) * f(x)=4x-3 / g(x)=x�+2x
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Question 745670: what is the equation for the sequence 31,26,21,16,11,...
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Question 747663: Find the general term an for the geometric sequence.
a1 = -2 and a2 = 6

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Question 747683: A theater has 49 seats in the first row, 53 seats in the second row, 57 seats in the third row, and so on. Answer the following questions:
1) Can the number of seats in each row be modeled by an arithmetic or geometric sequence? (which type of sequence is it)
2) Write the general term for a sequence an that gives the number of seats in row n.
3) How many seats are there in row 18?
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