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 1120323: For a geometric series, S2 = 20 and S3= 65. Find the first 3 terms.
Click here to see answer by ikleyn(52788)

Question 1120323: For a geometric series, S2 = 20 and S3= 65. Find the first 3 terms.
Click here to see answer by greenestamps(13200)

Question 1120340: 5 6 9 20 ? 414
What is the missing number
Click here to see answer by ikleyn(52788)

Question 1120335: what is the harmonic sequence of 3/2, 1/2, 3/10, 3/14... n= 9?
Click here to see answer by Edwin McCravy(20056)

Question 1120489: Hey,
I was hoping that you guys would be able to help me with a problem that I've been stuck on.
sum^31_(k=3) (1/k - 1/(k+1))
Sorry, didn't know how to do it in Latex.
Any help would be greatly appreciated!
Thanks,
SaturnV_
Click here to see answer by ikleyn(52788)

Question 1120725: 7, 16, 8, 27, 9,
Click here to see answer by greenestamps(13200)

Question 1120725: 7, 16, 8, 27, 9,
Click here to see answer by josgarithmetic(39618)

Question 1120724: 3, -6, 12, 4, 20,
Click here to see answer by greenestamps(13200)

Question 1120744: discuss how you will find the sum of the series:
1/2 + 1/4 + 1/8+ ... + 1/512
* our topic focuses on harmonic and fibonacci sequence but it can be other types of sequences or series :-)
Click here to see answer by rothauserc(4718)

Question 1120794: select the first five terms of the sequence.
an=4(2n-3)
Click here to see answer by josgarithmetic(39618)

Question 1120860: Ann goes swimming regularly she wants to improve her fitness, so she
decides to swim 10 lengths in the first session and increase the number of
lengths she swims by 2 every session. When she reaches 50 lengths in a
session, she will not increase the number any further. If Ann asks her
friend Joy to come swimming with her, Joy starts coming at Sue's 8th
session, Joy starts to swim 15 lengths and increases the number of
lengths by 5 each time. After how many of Joy's sessions does she swim
the same number of lengths as Ann?

Click here to see answer by greenestamps(13200)

Question 1120996: Find the first four terms of each sequence.
a1=-3
an=2n.an-1, if n is >1.
Click here to see answer by Tatiana_Stebko(1539)

Question 1121003: Find the next four terms of these sequences
1,2,5,10,17,_,_,_,_
1,1,2,3,5,8,13,21,_,_,_,_
Click here to see answer by Edwin McCravy(20056)

Question 1121010: 3, -6, 12, 4, 20, ?
7, 16, 8, 27, 9, ?
2, 7, 26, 101, 400, ?
7, 21, 8, 72, 9, ?

Click here to see answer by greenestamps(13200)

Question 1121010: 3, -6, 12, 4, 20, ?
7, 16, 8, 27, 9, ?
2, 7, 26, 101, 400, ?
7, 21, 8, 72, 9, ?

Click here to see answer by Alex.33(110)

Question 1121015: The first three terms of an infinite geometric sequence are m−1, 6, m+4, where m∈ℤ
Write down an expression for the common ratio, r.

Click here to see answer by greenestamps(13200)

Question 1121032: S(x)=1+5(x−5)+25(x−5)^2+125(x−5)^3+⋯.
Giving your answer as an interval, find all values of x for which the series converges.
Now assuming that x is within that interval above, find a simple formula for S(x)
Click here to see answer by ikleyn(52788)

Question 1120719: Find formula for the expression. Use sigma notation.
(x+(1/y))^n
Click here to see answer by Edwin McCravy(20056)

Question 1121118: Let {an}∞n=1 be a sequence whose partial sums are {Sn}∞n=1. Suppose that a1=2 and an=4⋅an−1.
Find a general formula for the nth term of the sequence of partial sums.
Click here to see answer by greenestamps(13200)

Question 1121187: I have generated the following number series using a very simple method that includes only addition. I will pay five dollars to anyone who can tell me the method I used and the next number in the series. Another five dollars for the number after that. Anyone?
6,13,6,9,12,5,12.......
Same method, slightly altered 15,12,19,12,15,18,11....
Good luck!
Dan
Click here to see answer by ikleyn(52788)

Question 1121366: The fourth term of a G.P. is 48 and the seventh term is 384.Find the common ratio and hence calculate the sum of the first six terms.
Click here to see answer by josgarithmetic(39618)

Question 1121494: 2 5 7 5 15 5 10
Click here to see answer by ikleyn(52788)

Question 1121584: What�s the sequence of 13,7,1,-5
Click here to see answer by Boreal(15235)

Question 1121589:
Click here to see answer by Alan3354(69443)

Question 1121697: If the given terms are part of an arithmetic sequence, write a rule for the sequence, then find a9
a1=1/2 and a23= 6
Click here to see answer by josgarithmetic(39618)

Question 1121696: If the given terms are part of an arithmetic sequence, write a rule for the sequence, then find a9
A1=-5 and a7= 91
Click here to see answer by josgarithmetic(39618)

Question 1121695: If the given terms are part of an arithmetic sequence, write a rule for the sequence, then find a9
A1=3 and a14= -23
Click here to see answer by josgarithmetic(39618)

Question 1121694: If the given terms are part of an arithmetic sequence, write a rule for the sequence, then find a9
A1=11 and a5=27
Click here to see answer by josgarithmetic(39618)

Question 1121709: The sum of 12 terms of an arithmetic series is 1212. The first term �a� and the common difference �d� are both whole numbers. Write down the first three terms of the series
Click here to see answer by greenestamps(13200)

Question 1121855: 3,-6,12,4,20 ?
13
14
6
16
Click here to see answer by greenestamps(13200)

Question 1121855: 3,-6,12,4,20 ?
13
14
6
16
Click here to see answer by MathTherapy(10552)

Question 1121858: The following are defined using recursion formulas. Write the first four terms of each sequence.
a1 = 7 and an = an-1 + 5 for n ≥ 2

Click here to see answer by greenestamps(13200)

Question 1121886: 7,5,2,14,3,1,2,6,8,5,3,16,6,2,4,_____?
Help!
Click here to see answer by Boreal(15235)

Question 1121961: The partial sum in the arithmetic series with first term 17 and a common difference of 3 is 30705. How many terms are there in the series?
Click here to see answer by ikleyn(52788)

Question 1121963: An arithmetic sequence a1,a2,......a100 has a sum of 15 000. Finf the first term and the common difference if the sum of the terms in the sequence a3, a6, a9,... a99 is 5016.
Click here to see answer by ikleyn(52788)

Question 1122041: What is next in the sequence: 9, 12, 7, 105, ___
Thanks
Click here to see answer by Alan3354(69443)

Question 1122124: What�s the next number in this sequence 22,66,68,34,102,104,52
Click here to see answer by math_helper(2461)

Question 1122290: the sum of four arithmetic means between 2 and -10 is______
Click here to see answer by greenestamps(13200)

Question 1122291: the sample space for tossing a coin is _______
Click here to see answer by Boreal(15235)

Question 1122289: sample space for tossing a coin once is _________
Click here to see answer by ikleyn(52788)

Question 1122347: The top level of a pyramid has 1 block. The next level has 3 blocks and the next level has 9 blocks. If this pattern continues, how many levels are there if the total number of blocks is 3,280?
Click here to see answer by solver91311(24713)

Question 1122358: Series 1 2 8 48 384 what is next

Click here to see answer by solver91311(24713)

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