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 1108437: If the 6th term of an AP is -10 and 10th term is -26. Determine the 15th term of an AP.
Click here to see answer by TeachMath(96)

Question 1108441: t3 = 20, t6 = 160, s5 = ?.
The third term is 20 and the sixth term is 160. What is the sum of the first 5 terms. This is part of geometric series questions so can you plz show me how to do it using formulas.
Thankyou
Click here to see answer by KMST(5328)

Question 1108491: What�s the answer of this in sigma notation.
2/3)+(3/4)+4/5+5/6+6/7
Click here to see answer by stanbon(75887)

Question 1108567: What is the fifth term of a geometric sequence whose first term is 32,768 and common ratio is one fourth?
Click here to see answer by Theo(13342)

Question 1108530: 6250 + 1250 + 250 + ... +2
Click here to see answer by rothauserc(4718)

Question 1108645: Find 50th term in arithmetic sequene
1/3, 1/9, 1/27, 1/81, 1/243
Click here to see answer by josgarithmetic(39617)

Question 1108664: 5,2.,6,4,7,8,8,?,9
Click here to see answer by josgarithmetic(39617)

Question 1108687: What is the common difference for the sequence :
4, 8/3, 16/9, 32/81, 64/6561

Click here to see answer by ikleyn(52787)

Question 1108766: Consider the sequence where tn = 15 − 5n and the sum of the first m terms is −1250.
Find the value of m.
Click here to see answer by greenestamps(13200)

Question 1108767: For an arthmetic sequence with t6 = -24 and t14 = 6. Find S10.
(6th term is -24, 14th term is 6, hence find the sum of the first 10 terms)
Click here to see answer by josgarithmetic(39617)

Question 1108765: Express 1.234 (with the 34 recurring) as a fraction in simplest form.
Click here to see answer by greenestamps(13200)

Question 1108801: A man was charged 2 cents per month for every 1 dollar he borrowed from a bank.At what rate per annum was he charged
Click here to see answer by ikleyn(52787)

Question 1108867: If n(A) = 4, n(B) = 5, and n(C) = 6, what is the greatest and least number of elements possible in AᑎBᑎC?

Click here to see answer by Edwin McCravy(20056)

Question 1109081: If the 4
th term of a AP is 16 and the 8
th term is 28
Find:- a) the first term
b) the common difference
c) The 16th term
Click here to see answer by ikleyn(52787)

Question 1109081: If the 4
th term of a AP is 16 and the 8
th term is 28
Find:- a) the first term
b) the common difference
c) The 16th term
Click here to see answer by TeachMath(96)

Question 1109080: Find the S20 if T3 = 19 and T8 = 44.
Click here to see answer by ikleyn(52787)

Question 1109080: Find the S20 if T3 = 19 and T8 = 44.
Click here to see answer by TeachMath(96)

Question 1109139: For what values of n will the infinite series (2n-1)+(2n-1)^2+...+(2n-1)^i+... have a finite value
Click here to see answer by ikleyn(52787)

Question 1109176: Coefficient of x in expansion of (x+3)5
Click here to see answer by Alan3354(69443)

Question 1109177: Coefficient of b in expansion of (3+b)4
Click here to see answer by Alan3354(69443)

Question 1109178: 2nd term in expansion of (y-2x)4
Click here to see answer by Alan3354(69443)

Question 1109173: Binomial Theorem :
Coefficient of x2 in expansion of (2+x)5
Click here to see answer by Alan3354(69443)

Question 1109175: Binomial Theorem :
Coefficient of x3y2 in expansion of (x-3y)5
Click here to see answer by Alan3354(69443)

Question 1109180: 2nd term in expansion of (y-x)4
Click here to see answer by Alan3354(69443)

Question 1109174: Biomial Theorem :
Expand Completely : ( y3-4x)3
Click here to see answer by Alan3354(69443)

Question 1109179: Find 1+2+3+4+...+140, the sum of the first 140 natural numbers
Click here to see answer by ikleyn(52787)

Question 1109179: Find 1+2+3+4+...+140, the sum of the first 140 natural numbers
Click here to see answer by Alan3354(69443)

Question 1109181: Expand completely (2x3+1)5
Click here to see answer by MathLover1(20850)

Question 1109181: Expand completely (2x3+1)5
Click here to see answer by greenestamps(13200)

Question 1109265: 51,62,83,86 what is the next number according this logic
Click here to see answer by greenestamps(13200)

Question 1109238: 1) the sum of the first 12 of an A.p is -96 and the Sum of the first 18th term is -252. find the
(a)common difference and
(b)the first term
2) How many terms of an A.p, 5,13,21............ give as sum of 275
Click here to see answer by Boreal(15235)

Question 1109379: Explicit formula the sequence & 12th term.
2, 6, 12, 20
Am I correct in having the formula be A(n)=n(n+1)?
This would make t he 12th term 156, right?
Thanks
Click here to see answer by KMST(5328)

Question 1109416: The sum of a finite geometric series.
Given n=6
-5, -15, -45, ...,
I worked this out and ended up with -1820 , but I am not sure the result is correct.
a1(1−r^n)/1−r
-5(1-3^6/1-2 = 3640/-2 = -1820
Please let me know if the formula I used was incorrect, thanks!

Click here to see answer by Boreal(15235)

Question 1109441: The 13th and 7th terms of an arithmetic sequence are 15 and 51 respectively

Which term is equal to-21?
Show that 66 is not a term of the sequence
Click here to see answer by josgarithmetic(39617)

Question 1109442: The first term and the last term of an arithmetic series is 5 and 61 respectively while the sum of all the terms is 975. Determine the number of terms in the series
Click here to see answer by ikleyn(52787)

Question 1109439: The sum of the first 4 terms of a geometric series is 15 and the sum of the next 4 terms is 240 determine the positive constant ratio

Click here to see answer by ikleyn(52787)

Question 1109504: The fifth term of an arithmetic sequence is 23 and the 12th term is 72. 1)Determine the first three terms of the sequence and the nth term? 2) what is the value of the tenth term 3) which term has a value of 268
Click here to see answer by josgarithmetic(39617)

Question 1109516: My Alegbra Mid term study guide has stumped me on this one question which is probably very simple I just haven't been in class. It says which shows a function for the sequence 16, 8, 4, 2...? The list of answers are ;
A. f(x) = 16 � (2)^x-1
B. f(x) = 16 (1/3)^x -1
C. f(x) = 16 � (1/2)^x-1
D. f(x) = 16 � (1/4)^x-1
I can't seem to understand which type of sequence it is or how to solve the question, I've googled so much and still can't get it

Click here to see answer by josmiceli(19441)

Question 1109576: Complete the series
889 859 834 814
Click here to see answer by Edwin McCravy(20056)

Question 1109670: The number of terms in an A.P. whose first term is 5, common difference 3, and sum 55 is
Click here to see answer by rothauserc(4718)

Question 1109826: I have been working on this problem for HOURS!!! Can anyone explain how to determine the next number?
Predict the next term in the series of numbers below and give the formula.
3,10,2,7,7
Thank you so much in advance!
Click here to see answer by ikleyn(52787)

Question 1110010: The xth, yth, and zth terms of a sequence are X,Y,Z respectively. Show that if the sequence is arithmetic then X(y-z) + Y(z-x) + Z(x-y)=0.

Click here to see answer by AnlytcPhil(1806)

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