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 734289: If 111 equals 13 and 112 equals 24 and 113 equals 35 and 114 equals 46 and 115 equals 57, then what does 117 equal?
Click here to see answer by MohammedP(1)

Question 734289: If 111 equals 13 and 112 equals 24 and 113 equals 35 and 114 equals 46 and 115 equals 57, then what does 117 equal?
Click here to see answer by Alan3354(69443)

Question 748064: Find the general term an for the sequence where a3= -45/16 and r=-3/4
Click here to see answer by reviewermath(1029)

Question 748043: Evaluate each geometric series:
-2-6-18-54..., N=7

Click here to see answer by nerdybill(7384)

Question 748250: For the following series, express the finite sum in summation notation:
3 − 9 + 27 − 81 + 243 − 729
Click here to see answer by tommyt3rd(5050)

Question 748256: What number continues the sequence 368 406 452 494 538?
Click here to see answer by MathLover1(20850)

Question 748283: If the first term of an arithmetic sequence is 4 and the third term is 18, what is the 23rd term?
A.92
B.116
C.158
D.161
Click here to see answer by reviewermath(1029)

Question 748365: What is the first 3 sequences of this equation? an = 7 + (n - 1)5
Click here to see answer by solver91311(24713)

Question 748728: If you could help i would really appreciate it!!!
Find the number of terms in the geometric series with
Sn=218.6765, t1=4, and r=1.05
Thank you so very much!!
Click here to see answer by reviewermath(1029)

Question 748956: I would really like if you can solve this for me.
For a set of six integers, the Mode is 8, the Median is 9 and the Mean is 10.
The smallest integer is greater than 6 and the largest integer is 16.
Find the two possible sets of six integers.
I am sorry if it is a silly question but I would really appreciate your help.
Click here to see answer by reviewermath(1029)

Question 749205: Please help me solve this problem:
Show that
(n + 1) !
______ = n^3 - n for n equal or greater than 2.
(n - 2)
To use this equation for n =1, explain why it is necessary to define 0! = 1 ( this is a standard definition of 0!).
Click here to see answer by solver91311(24713)

Question 749554: What is the seventh term of this sequence? 2, -10, 50, -250

Click here to see answer by rfer(16322)

Question 749576: find the equation of the sequence....
-6, 24, -96.....
Click here to see answer by stanbon(75887)

Question 749623: how do i find the recursive formula: 20,30,40,50...
Click here to see answer by tommyt3rd(5050)

Question 749654: A car used 3t gallons of gasoline to travel 5 miles. How many gallons of gasoline are needed to travel 8 miles?

Click here to see answer by stanbon(75887)

Question 749860: Dear Tutor,
which is the next number in this row: 2, 6, 30, 168, 1320? Thank you very much and
Best regards,
Decebal Paltanea
Romania
Click here to see answer by Edwin McCravy(20056)

Question 749910: 1. The 100th Term is -354 the difference is -6 whats the first term?
I dont understand how to even start this. I don't even understand the
An=a1+d(n-10 and I dont understand Sn=n(a1+an)/2
Click here to see answer by Edwin McCravy(20056)

Question 749911: Write the following as a summation and find the sum of the series (3-1)+(1/3-1/9)+....
Click here to see answer by reviewermath(1029)

Question 750008: Evaluate each infinte geometric series.
http://assets.openstudy.com/updates/attachments/5196dbd0e4b0e2ba86d44757-helperoc101-1368841201531-sdfds.png

Click here to see answer by reviewermath(1029)

Question 750011: Evaluate each infinite geometric series.
http://assets.openstudy.com/updates/attachments/5196e052e4b0e2ba86d44a29-helperoc101-1368842331108-untitled256.png
Click here to see answer by reviewermath(1029)

Question 750086: I have a question which goes like this:
An = 2-A*n-1, where A5 = 3. I need to find the tenth value. The answer is -1 but I don't know exactly how to do it.
Can you please help me out?
Thank you
Click here to see answer by rothauserc(4718)

Question 750265: 5/8+12=
Click here to see answer by FrankM(1040)

Question 750276: 1 less than 400% of a number

Click here to see answer by tommyt3rd(5050)

Question 750467: Please help me
Find the fractions equal to the given decimals
1. 0.82222...
Click here to see answer by Alan3354(69443)

Question 750467: Please help me
Find the fractions equal to the given decimals
1. 0.82222...
Click here to see answer by DrBeeee(684)

Question 750464: Please help with me
Find the fractions equal to the given decimals
1. 0.55555
Click here to see answer by jim_thompson5910(35256)

Question 750465: Find the fractions equal to the given decimals
1. 0.70707
Click here to see answer by tommyt3rd(5050)

Question 750549: Starting with n=1, find the first 5 terms of: .
Please explain the steps the best that you can. Thanks. :)

Click here to see answer by MathLover1(20850)

Question 750669: how many terms are needed to make the sum of 4+17/4+9/2+... first exceed 80?
Click here to see answer by MathLover1(20850)

Question 750716: complete the series 18,32,50,72
Click here to see answer by josgarithmetic(39618)

Question 750752: Find the 24th term of the arithmetic sequence whose common difference is 2 and whose first term is 4.
Click here to see answer by timvanswearingen(106)

Question 751099: find the 9th term of a geometric progression whose 4th and 7th terhs are -4 and 256 respectively
Click here to see answer by stanbon(75887)

Question 751294: Find the seventh term of the geometric sequence 1,1/5,1/25
Click here to see answer by reviewermath(1029)

Question 751306: The product of two consecutive integers is 9 less than 9 times their sum. Find the integers. I would like to know how to do this problem
Click here to see answer by stanbon(75887)

Question 751318: The area of a square is numerically 77 more than the perimeter. Find the length of the side
Click here to see answer by reviewermath(1029)

Question 751451: Please help me,
solve the given problems involving factorials
Show that
( n+ 1) !
------ = n ^3 - n for n ≥ 2
(n - 2) !
Click here to see answer by reviewermath(1029)

Question 751737: A side of an equilateral triangle is 10 cm. the midpoints of its sides are joined to form an inscribed equilateral triangle, and this process is continued. Find the sum of the perimeters of the triangles if the process is continued without end.
Click here to see answer by reviewermath(1029)

Question 751785: Please help me
Find the first four terms of the indicated expansions
( 2x^2 + y/3) ^15
Click here to see answer by stanbon(75887)

Question 752003: For questions 3-5, find the first 4 terms and the 8th term of the recursively-defined sequence.
3. b1 = 2 and bk+1 = 3bk, for k>0

4. v1 = 0.75 and vn = (-2)vk-1 for n>1

5. c1 = 2, c2 = -1, and ck+2 = ck + ck+1 for k>0

Click here to see answer by stanbon(75887)

Question 752134: I don't recall viewing any similar problems during the series and sequences unit this year, so any help would be appreciated.
How many license plates can be made if they are formed by 3 letters, followed by 3 digits, followed by a letter? Digits and letters may be repeated.
Click here to see answer by josmiceli(19441)

Question 752230: Given the first term, a1, the common difference, d , and the arithmetic sequence a1 = 6, d = 8, the 20 th term would be?
Click here to see answer by stanbon(75887)

Question 752300: Write the first four terms of the geometric sequence satisfying the following conditions: a2 = 11, and a3 = -121
Click here to see answer by reviewermath(1029)

Question 752362: Find the sum of the first 5 terms of the sequence defined by an = -7(-4)n − 1 for n ≥ 1.
Click here to see answer by stanbon(75887)

Question 752367: 5,10,15,30, 35, 70, , ,
Click here to see answer by FrankM(1040)

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