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

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Question 628857: Please write out the forumla for $43.00 less 1%
Click here to see answer by richwmiller(17219)

Question 628919: xyz+zyx=686
In the correctly solved addition problem above, the letters X,Y, and Z represent different nonzero digits. What is the value of x+y+z?
Please include explanations!
Click here to see answer by ankor@dixie-net.com(22740)

Question 629213: prepare 2L of a 25% alcoho solution and a 15% alcohol
Click here to see answer by Alan3354(69443)

Question 629654: The mean of a list of 80 nos. is 230. If the four nos. 145,156,210 and 255 are added, what is the mean of the list of nos.
I asked this question yesterday and have been pondering it since then. I think I have the solution but would you check it for me please.
Sum of 80 nos. is 18,400 80*230
Sum of 4 nos added is 766
Mean of new list is 19166/84=228.17
Thank you
Click here to see answer by ewatrrr(24785)

Question 629698: name all the sets of numbers to which each real numbers belongs. let n= natural numbers,w= whole numbers, z= integers, q=rational numbers, and i= irrational numbers /25 answers a:z,q b:n,z,q c:w,z,q d;n,w,z,q
Click here to see answer by jim_thompson5910(35256)

Question 629700: order each sets of numbers from greatest to less/43,3.6-3/2 / is square root symbol answers a:-3/2,3.6,/43 b:-3/2, /43,3.6 b:-3/2,/43,3.6 c:/43,3.6-3/2 d:3.6-3/2,/43
Click here to see answer by ewatrrr(24785)

Question 629829: What is the common difference of a 43-term arithmetic sequence where the first term is -13 and the sum is 9,374?
What is the sum of a 12-term arithmetic sequence where the last term is 13 and the common difference is -10?
Provide an example of an arithmetic series which totals zero. Using complete sentences, explain how you created the example

Click here to see answer by reviewermath(1029)

Question 630235: What is the next term for the given arithmetic sequence?

-3, -2.25, -1.5, -0.75, ...
Click here to see answer by ewatrrr(24785)

Question 630585: A tugboat goes 180 miles upstream in 15hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without a current and the speed of the current
Click here to see answer by josmiceli(19441)

Question 630701: find the next term in the sequence 5, 8, 12, 17
Click here to see answer by Tatiana_Stebko(1539)

Question 630806: Find the rational number represented by the repeating decimal.
__
0.58 =
Click here to see answer by stanbon(75887)

Question 630804: Find the nth term, the fifth term, and the eighth term of the geometric sequence.
8,4,2,1....
an=
a5=
a8=
Click here to see answer by dfrazzetto(283)

Question 630801: Find the number of terms in the arithmetic sequence with the given conditions.
a1=-3, d=1/3, S=55
n=
Click here to see answer by stanbon(75887)

Question 630807: Without expanding completely, find the sixth term in the expansion of the expression.
((1/c)+(c^2/2))^8
Click here to see answer by stanbon(75887)

Question 631049: Find the first five terms of the recursively defined infinite sequence.
a1=2, ak+1=3ak-4
a1=
a2=
a3=
a4=
a5=
Click here to see answer by dfrazzetto(283)

Question 631054: Use synthetic division to find the quotient and remainder if the first polynomial is divided by the second.
3x^3-3x^2+4x-5; x-5
quotient=
remainder=
Click here to see answer by stanbon(75887)

Question 631051: Find the common difference for the arithmetic sequence with the specified terms.
a4=10, a11=38
d=
Click here to see answer by stanbon(75887)

Question 631053: Without expanding completely, find the sixth term in the expansion of the expression.
((1/c)+(c^2/2))^8
Click here to see answer by ewatrrr(24785)

Question 631061: Find the first five terms of the recursively defined infinite sequence.
a1=2, ak+1=3ak-4
a1=
a2=
a3=
a4=
a5=
Click here to see answer by stanbon(75887)

Question 631110: a bicycle wheel rotates 300 times in a minute as long as the rider is pedaling. If the rider stops pedaling, the wheel starts to slow down. Each minute it will rotate only 2/3 as many times as in the preceding minute. how many times will the wheel rotate in the 4th minute after the rider's feet leaves the pedals? Round your answer to the nearest unit.
Click here to see answer by josmiceli(19441)

Question 631115: Use the Binomial Theorem to find the coeficient of 1/x in the expansion of (2x + 1/x)^3
Click here to see answer by Alan3354(69443)

Question 631183: if,
1=5
2=25
3=325
4=4325
5=?
Is it equal to 1? or 54325?
Click here to see answer by Alan3354(69443)

Question 631183: if,
1=5
2=25
3=325
4=4325
5=?
Is it equal to 1? or 54325?
Click here to see answer by ewatrrr(24785)

Question 631367: what is the next number in the series 5 10 15 25 40 ?
Click here to see answer by sachi(548)

Question 631366: what is the next number in the series 40 39 35 40 30 41 ?
Click here to see answer by sachi(548)

Question 631372: If the 4th term of the geometric progression is -32 and the 7th term is 108,what is the 9th term?
Click here to see answer by sachi(548)

Question 631409: the next three terms in these geometric sequences and how you getted
1,0.4,0.16,0.016
Click here to see answer by dfrazzetto(283)

Question 631818: someone please help me with this! ive tried a bunch of times and cant figure it out!
write each sum using summation notation.
Q1) 2 + 5 + 8 + 11 + ... + 29
Q2) 6 - 12 + 24 - 48 + ...

find the first 4 terms and the 8th term of the recursively-defined sequence.
Q1) c1 = 2, c2 = -1, and ck+2 = ck + ck+1 for k>0
Click here to see answer by ewatrrr(24785)

Question 631827: 1)Find the sum of the arithmetic sequence 2, 4, 6, 8, ..., 70.
2)Find the sum of the geometric sequence 42, 7, 7/6, .... , 42(1/6)^8
3)find the sum of the first n terms of the sequence. The sequences are either arithmetic or geometric. -1, 11, -121, ...; n = 9
4)find the sum of the first n terms of the sequence. The sequences are either arithmetic or geometric. 14, 8, 2,...; n=9
Click here to see answer by ewatrrr(24785)

Question 631826: i really need help with this! i already got on tutor.com and didnt understand how they explained it! can someone help?!?!
1)Find the sum of the arithmetic sequence 2, 4, 6, 8, ..., 70.
2)Find the sum of the geometric sequence 42, 7, 7/6, .... , 42(1/6)^8
3)find the sum of the first n terms of the sequence. The sequences are either arithmetic or geometric. -1, 11, -121, ...; n = 9
4)find the sum of the first n terms of the sequence. The sequences are either arithmetic or geometric. 14, 8, 2,...; n=9
Click here to see answer by ewatrrr(24785)

Question 631823: can someone please help?! ive tried a bunch of times and cant find the answers!!!
Identify the sequence {-2, 2, -2, 2 …} as arithmetic or geometric. Then find the common difference or ratio as appropriate.
Identify the sequence {-5, -2, 1, 4 …} as arithmetic or geometric. Then find the common difference or ratio as appropriate.
The third and sixth terms of a geometric sequence are -75 and -9375 respectively. Find the first term, the common ratio, and an explicit rule for the nth term.
Determine whether the infinite series 1/64 + 1/32 + 1/16 + 1/8 + ..... is equal to a real number. If so, find the sum.
Click here to see answer by solver91311(24713)

Question 631899: Suppose that a sequence is defined as follows.
a[1] = -1 , a[n] = -3a[n-1]+6 for n ≥ 2
list the first terms of the sequence?
Click here to see answer by ewatrrr(24785)

Question 631899: Suppose that a sequence is defined as follows.
a[1] = -1 , a[n] = -3a[n-1]+6 for n ≥ 2
list the first terms of the sequence?
Click here to see answer by solver91311(24713)

Question 632016: Please help me solve this problem:
Find the eight term in the expansion of (a + b)10
thank you!
Click here to see answer by nerdybill(7384)

Question 632068: Find the missing term in the sequence 4/3, 3/4, 1/6, ____.
Click here to see answer by ewatrrr(24785)

Question 632106: what is the first five terms of the sequence an = 2^n
Click here to see answer by ewatrrr(24785)

Question 632460: 5
E i(i-5)(i-3)
i=0
Find the sum of the series. I am not sure the steps to solve.
Click here to see answer by stanbon(75887)

Question 633219: Consider the recursive sequence. a1=3, a2=5, an = 1/2(an-1+an-2)
Find a3, a4, and a5.
Click here to see answer by ewatrrr(24785)

Question 633232: Find the nth term of the geometric sequence.
0.3, 0.03, 0.003, ...
Click here to see answer by stanbon(75887)

Question 633283: I need help figuring out how to solve this.
It is an infinite series, 1+3+9+27+81+243+...= -1/2
I need to prove that this infinite series equals -1/2.
Click here to see answer by Alan3354(69443)

Question 633231: Prove nn^2 for n>=4 and nn^3 for n>=6 by using Principle of Mathematical Induction.
Click here to see answer by Edwin McCravy(20056)

Question 633227: Prove a^n -1=(a-1)(a^(n-1) + a^(n-2) +.......+ a+1) by using Principle of Mathematical Induction.
Click here to see answer by KMST(5328)

Question 633416: If the unit's digit in the product (47x*729*345*343) is 5,what is the maximum number of values that x may take?
Click here to see answer by Edwin McCravy(20056)

Question 633551: Find the nth term of the geometric sequence.
-4, 20, -100, ...
Click here to see answer by ewatrrr(24785)

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