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 39633: I'm not sure this is the right forum to ask but I would like to find out what number comes next in this sequence? 3692, 738, 584, 232, ???
Thanks for your help!
enjel
Click here to see answer by atif.muhammad(135)

Question 40061: Use the indicated property to write an expression that is equivalent to the following expression.
(7 + 11) + 2 (associative property of addition)
Click here to see answer by fractalier(6550)

Question 40302: Hello!
Here's a tutor who is a bit rusty on this subject. Is there a simple expression for the following sum?

For example,
1 + 4 + 9 + 16 + ... + 100
or
25 + 36 + 49
etc.
Thank you very much!
Click here to see answer by venugopalramana(3286)

Question 40523: factor completely
3x2+16x+20
Click here to see answer by josmiceli(19441)

Question 40853: a1= 2
r= 3
Formula is Sn =
Here n =6, so S6 = = 728
Click here to see answer by psbhowmick(878)

Question 40979: solve the arithmetic sequence
a5=-2 and a13=30
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Question 40980: find the sum of the first n terms of the given arithmetic series
a1=-13,a7=20.8 (n=7)
Click here to see answer by stanbon(75887)

Question 41117: Find the sum of the geometric Series: 4,-2,-1/2,.....Answer should be a fraction.
Click here to see answer by stanbon(75887)

Question 41115: Find the third term in the expansion of:(e-2f)^8
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Question 41611: Use the Binomial Theorem to find the third term in the expression of (n-2p)^6.
Thanks
Click here to see answer by venugopalramana(3286)

Question 41742: what are the next two numbers in this sequence and what is the difference between the terms:
3, 7, 14, 23, 36, _, _
Click here to see answer by abcdefg(37)

Question 41799: Use the binomial theorum to find the fifth term in the expansion (2x+3y)^5.
Thank You
Click here to see answer by fractalier(6550)

Question 41798: Find the first three iterates x(1), x(2), x(3) of f(x) = 2x-5 for an initial value of x(0) = 3.
Thank You
Click here to see answer by fractalier(6550)

Question 41795: Find the sum of the infinite geometric series 36 + 24 + 16 +... if it exists
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Question 41801: Find a counter-example to the statement 4^n+1 is divisible by 5.
Thank You
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Question 41796: Find the first five terms of the sequence for which a(1)=5 and a(n+1)= 3a(n)+1.
Thank You
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Question 41806: Students are given a list of ten vocabulary words to learn. In how many ways could four of the words be listed on a test?
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Question 41805: A scout troop will prepare trail mix for their next hike. They have decided to mix one type of nut, one type of dried fruit, and one type of granola. The local store carries 8 types of nuts, 6 types of dried fruit, and 5 types of granola. How many different trail mixes are possible?
Thanks
Click here to see answer by fractalier(6550)

Question 41935: Find the sum of a geometric series for which a(1)=1, r=2, and n=6
Thanks you
Click here to see answer by fractalier(6550)

Question 41934: Find four geometric means between 4096 and 972.
Thank you
Click here to see answer by fractalier(6550)

Question 41934: Find four geometric means between 4096 and 972.
Thank you
Click here to see answer by AnlytcPhil(1806)

Question 41933: Find the next two terms of the geometric sequence 6250,5000,4000,...
Click here to see answer by fractalier(6550)

Question 41936: Find a(1) in a geometric series for which S(n) =189, r=1/2, and a(n)=3.
Thank you
Click here to see answer by venugopalramana(3286)

Question 41931: Find the three arithmetic means between 21 and 13.
Click here to see answer by fractalier(6550)

Question 41932: Find S(n) for the arithmetic series in which a(1)=-11, a(n)=13, and n=7.
Thank you
Click here to see answer by venugopalramana(3286)

Question 41932: Find S(n) for the arithmetic series in which a(1)=-11, a(n)=13, and n=7.
Thank you
Click here to see answer by fractalier(6550)

Question 41804: Find a(1) in a geometric series for which S(n) = 189, r = 1/2, and a(n) =3.
Thanks
Click here to see answer by venugopalramana(3286)

Question 42050: Please sir , send me the value or method to find the value of the following summation.

sum of ( a^n * b^n ) / (n ! )2

here a and b are non negative real constants and summation is over n where n varies 0 to infinity.
Click here to see answer by psbhowmick(878)

Question 42186: 256, 64, 16, 4..
is this sequence geometric, arithmetic, or neither
Click here to see answer by psbhowmick(878)

Question 42187: -64, 32,-16, 8,-4
is this sequence geometric, arithmetic, or neither
Click here to see answer by psbhowmick(878)

Question 42189: 1/12, 2/13, 3/14, 4/15...
is this sequence geometric, arithmetic, or neither
Click here to see answer by psbhowmick(878)

Question 42475: what are the rules governing the operation on si
gned numbers?
Click here to see answer by rapaljer(4671)

Question 42557: How many four-digit numerical codes can be created if no digit may be repeated?
Thanks
Click here to see answer by psbhowmick(878)

Question 42555: Find the sum of the infinite geometric series: 1 + 3/5 + 9/25 + ..., if it exists.
Thanks
Click here to see answer by psbhowmick(878)

Question 42556: Use the Binomial Theorem to find the sixth term in the expansion of (m+2p)^7.
Thanks
Click here to see answer by psbhowmick(878)

Question 41753: A.Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
Include the following in your answer:
b.Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
c.Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?
d.Give at least two real-life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally.
I don't understand this question.Can someone please help this is recking my brain.
Click here to see answer by astromathman(21)

Question 42841: The sequence 2,3,5,6,7,10,... consists opf all natural numbers which are neither perfect squares nor perfect cubes. Find the 75th term of this sequence?
Click here to see answer by fractalier(6550)

Question 42912: Determine the sum for the geometric series 1/2 - 1/3 + 2/9 - 4/27 +...
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Question 42939: write the sigma noation for the series sonsisting of positive two-digit intergers ending in 2
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Question 42956: determine the sum for the positive two-digit integers that are not divisible by 5
Click here to see answer by fractalier(6550)

Question 41710: Find the next two terms of the geometric sequence 6250, 5000, 4000,...
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Question 43315: Write out the first five terms of the sequence given by:
ok HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
a_n=n^2-n
first n is a subsc.
a. 0, 2, 6, 12, 20
b. 2, 6, 12, 20, 30
c. 1, 4, 9, 16, 25
d. 0, 3, 8, 15, 24
e. None of the others

Click here to see answer by psbhowmick(878)

Question 43317: I just don't even know what to say..................help!!!!!!!!!!!!!!!!!
Given the following recursively defined sequence, find the fifth term.
a_1 = -4
a_2 = -4
a(_n+2)= a(_n+1)-4a_n
a. 28
b. 764
c. -20
d. -308
e. None of the others

Click here to see answer by fractalier(6550)

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