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 1018511: if a1,a2,a3.... are in A.P Such tgat a2/a7=3/2, then the 13th term of A.P is

Click here to see answer by ikleyn(52788)

Question 1018511: if a1,a2,a3.... are in A.P Such tgat a2/a7=3/2, then the 13th term of A.P is

Click here to see answer by MathTherapy(10552)

Question 1018580: Simply the equations in the following sequence to fractions and solve for the 7th term in the sequence
1 + 1/4 , 1 + 1/1 + 1/4, 1 + 1/1 + 1/1 + 1/4

Click here to see answer by ikleyn(52788)

Question 1018682: What should be the next letter in the following series azebiyo
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Question 1018681: What should be the next number in the following series 100 96 104 88 120 56
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Question 1018680: What should be the next number in the following series 1 2 8 48 384
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Question 1018776: For which values of x will ((-3x+5)/2)+(((-3x+5)/2)^2)+(((-3x+5)/2)^3)+... Be a converging series?
Click here to see answer by ikleyn(52788)

Question 1018776: For which values of x will ((-3x+5)/2)+(((-3x+5)/2)^2)+(((-3x+5)/2)^3)+... Be a converging series?
Click here to see answer by rothauserc(4718)

Question 1018879: Determine the first term of the arithmetic sequence in which the 16th term is 110 and the common difference is 7
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Question 1019223: what is the similarity between the numbers 85,17,19,4 and 2? from capital fm
Click here to see answer by Alan3354(69443)

Question 1019259: 1,-1,2,-6,24
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Question 1019254: what is the next number in the following sequence
3,-6,12,4,20
Click here to see answer by Edwin McCravy(20056)

Question 1019279: eexplain how does these patterns it works?
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Question 1019279: eexplain how does these patterns it works?
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Question 1019397: In a geometric progression coasting of positive terms each term equals to thw sum of the next two terms then the common ratio is

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Question 1019525: in a certain ap the 32nd term is twice the 12th term prove that 70th term is twice the 31st term

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Question 1019618: Starting with a sum of 4,638.40 I must find a way to subtract 25% from the sum a total of 162 times until I deplete the sum and enter negative numbers. I'm putting this into an Excel spreadsheet. It's been decades since I've been in math class. Which algebraic formula would I use? Thank you.
Click here to see answer by Boreal(15235)

Question 1019668: If the fifth term of an arithmetic sequence is 14 and second term is 5, find the 15th term.
thank you
Click here to see answer by stanbon(75887)

Question 1019763: Sam wrote the natural numbers from 1 to 5280 in order. What is the 6001st digit that Sam wrote?
Click here to see answer by FrankM(1040)

Question 1018961: Prove that:
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Question 1019813: what is the similarity between the numbers 85,17,19,4 and 2?
Click here to see answer by richard1234(7193)

Question 1019850: Find the equation of the lines which are equidistant from the lines y=2and y=-2
Click here to see answer by josmiceli(19441)

Question 1018520: a1=?
a2=4/15
a3=?
a4=?
a5-3/5
a6=?
a7=?
a8=-24/15
Click here to see answer by Fombitz(32388)

Question 1019949: If g(x) = (x+2)/3, find g(g(g(g(1)))).
Click here to see answer by robertb(5830)

Question 1019968: what is next in this sequence 20 /23 ,10/ 23 , 5 /23 , 5 /46
Click here to see answer by ikleyn(52788)

Question 1019968: what is next in this sequence 20 /23 ,10/ 23 , 5 /23 , 5 /46
Click here to see answer by robertb(5830)

Question 1019953: How do I write a recursive formula for the 20th term?

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Question 1020019: Please help me solve these question, in geometric progression. The first and the last term of the geometric progression are 2 and 2,048 respectively.The sum of the term of the progression is 2,730 find the number of terms and the common ratio (c.r)
Click here to see answer by robertb(5830)

Question 1020237: I am trying to find the steps to solve this one. Any help will be appreciated! Thanks!
Assume 12+24+36+...+12n=6n(n+1) is true for all positive integers n. If we add 12(n+1) to the left hand side, what is the value of the new right hand side?
Answer is: 6(n+1)(n+2)
Click here to see answer by robertb(5830)

Question 1020334: Find four geometric means between 486 and 2
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Question 1020460: Your help will be appreciated thanks!
Let a(1)=5. Define a(n) to be (a(n-1))/2 if a(n-1) is even, 3a(n-1)+1 if a(n-1) is odd for all other natural numbers n. What is the fourth term of the sequence?
Click here to see answer by ikleyn(52788)

Question 1020715: Let a and b be the 4th and 5th term of an arithmetic sequence, respectively. What is its 10th term in terms of a and b?
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Question 1020716: In an arithmetic sequence, the mth and nth term are n and m, respectively. What is its first term in terms of m and n?
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Question 1020722: 1+5+9+?+81
Click here to see answer by richard1234(7193)

Question 1020764: What is the nth term of the sequence (-1, 4, -9, 16, ......)?

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Question 1020784: Determine which term of the arithmetic sequence : 3, 5, 7...is equal to 27
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Question 1020885: The numbers in each of the three brackets
follow the same rule. Find the missing
number.
[19, 25, 3] [4, 26, 11] [?, 51, 9]
A 20
B 31
C 33
D 34
I cannot find any common rule?
Click here to see answer by MathLover1(20850)

Question 1020924: In a sequence of 10 terms as 10^10+10^10+...+10^10=10^x, what is x?
Click here to see answer by ikleyn(52788)

Question 1020957: 1, 3/4, 5/9, 7/16...
Click here to see answer by ewatrrr(24785)

Question 1020954: 2, 4, 8, 16...
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Question 1020956: 0, 2, 0, 2, 0...
Click here to see answer by Edwin McCravy(20056)

Question 1020960: If 2;x;18;... Are the first three terms of a geometric sequence determine the value(s) of x
Click here to see answer by robertb(5830)

Question 1021048: For each sequence, find a closed formula for the general term, a sub n.
a) -2,-8,-18,-32,-50
b)96,94,92,90,88
c)-58,-580,-5800,-58000,-580000
Click here to see answer by robertb(5830)

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