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 264758: 3+6+9+...+996+999=
1+3+3^2+3^3+...+3^30=
1+(-1)+(-1)^2+...+(-1)^1000=
Click here to see answer by stanbon(75887)

Question 264927: The sum of three consecutive natural numbers 1s 75. Find the three numbers.
Click here to see answer by josmiceli(19441)

Question 265252: Find "k" so when x^3 + kx^2 - kx + 1 is divided by x-2, the remainder is 0.
Click here to see answer by drk(1908)

Question 265498: What are the next two terms in each sequence?
1.3, 2.4, 3.5, 4.6, �
Click here to see answer by rfer(16322)

Question 265521: The sum of two numbers is less than or equal to 23 . The second number is 7 less than the first. What are the possible values for the first of the two numbers? I cannot come up with an answer for this one and I am getting frustrated can someone please help me, thank you.
Click here to see answer by roseo(33)

Question 265912: The nth term of a sequence is given by the formula n^2+2n How much larger is the 10th term of the sequence than the 9th term?

Click here to see answer by asuar010(338)

Question 265850: you want a sum of about 60. which 2 numbers would you add? 28/ 47/ 59/ 8
Click here to see answer by asuar010(338)

Question 265723: arithmetic sequence a10=x+3 a11=2x+7 a12=4x-2 which term equals 186
Click here to see answer by drk(1908)

Question 266257: Is 5,9,13,17,21
arithmeic or geometric sequence and what is the number that makes them go to the next number.
Click here to see answer by asuar010(338)

Question 266261: is 1,0.3,0.009,0.0027,0.0081 a geometric sequence or a arithmetic and what number is multiplied to get to the next

Click here to see answer by Alan3354(69443)

Question 266760: If someone could please help me with this problem, it would be greatly appreciated!
I have to find the sum of the geometric sequence
, , ...
This is what I have so far:
r=(1/3)

(it's supposed to be (n-1))
from this I got n=5

As elementary as this is, I need help finding the sum and understanding the process(es) of how to work this equation when fractions are in the mix. (That is, unless I've made mistakes prior to getting to this point.)

Click here to see answer by Edwin McCravy(20056)

Question 266763: Please help me solve this Geometric Sequence.
My teacher doesn't teach very well so it's kind of hard to comprehend everything.
equation-91st term: 1/5,-1/5,1/5,-1/5,1/5,...
Click here to see answer by drk(1908)

Question 267464: find the first six terms of arithmetic sequence
Click here to see answer by Edwin McCravy(20056)

Question 267871: Prove by mathematical induction: ∑_(i=1)^n (3^i= 3(3^n-1)/2)
Click here to see answer by Edwin McCravy(20056)

Question 268975: (2r^(-1)+s^(-1) )^5 Expand the Binomial.
Click here to see answer by persian52(161)

Question 268983: Insert K arithmetic means betweens the given numbers.
11/3 and 6; k=4
Click here to see answer by stanbon(75887)

Question 268983: Insert K arithmetic means betweens the given numbers.
11/3 and 6; k=4
Click here to see answer by drk(1908)

Question 269102: A sum of Rs.6240 is paid off in 30 instalments such that each instalment is Rs. 10 more than the proceeding instalment. the value of the 1st instalment is.
(A)Rs=36 (B)Rs=30 (C)Rs=60 (D) none of these.
Click here to see answer by checkley77(12844)

Question 269183: (2r^(-1)+ s^(-1))^5 Expand the sum of the two terms of a Binomial. Using the Binomial Theorem.
Click here to see answer by persian52(161)

Question 269823: Using any mathematical operations or grouping symbols, arrange eight 8s to equal 1000.

Click here to see answer by drk(1908)

Question 269823: Using any mathematical operations or grouping symbols, arrange eight 8s to equal 1000.

Click here to see answer by Edwin McCravy(20056)

Question 269980: Find the first five terms of each geometric sequence described.
1. a sub1=-1, r=-3
2. a sub1=-1/3, r=2
Click here to see answer by edjones(8007)

Question 270153: 3, 5,�5...
The first term in the sequence of numbers shown above is 3. Each even�numbered term is 2 more than the previous term and each odd�numbered term, after the first, is �1 times the previous term. For example, the second term is 3 + 2, and the third term is (�1) � 5. What is the 55th term of the sequence?
(A)�5 (B) �3 (C) �1 (D) 3 (E) 5

Click here to see answer by Edwin McCravy(20056)

Question 270616: State this term as arithmetic,geometric, fibonacci or none of these. Supply the next term as well? 9,3,1,____?
Click here to see answer by edjones(8007)

Question 270658: In the sequence, 1^1, 2^4, 3^9, 4^16, .......9^n, find the value of n.
Click here to see answer by Greenfinch(383)

Question 270608: Find the sum of the first n positive integers?
Click here to see answer by rfadrogane(214)

Question 270610: Find the sum of the first 100 even positive integers?
Click here to see answer by rfadrogane(214)

Question 271050: 1,1,2,3,5,8,... find the next five terms of the Fibonacci sequence
Click here to see answer by stanbon(75887)

Question 271227: Ineed some helpw with the following two questions...
1. Compute the sum of the following unsigned integers. 0b11000100 + 0b00110110

2. How many bits are required to represent the decimal number 1497 as unsigned binary integer?

Click here to see answer by Stitch(470)

Question 271688: An arithmetic series has 20 terms. The first is -50 and the last term is 83, find the sum of the series
Click here to see answer by checkley77(12844)

Question 271966: 5, 8, 12, X, 34, 55, 89..... The value of X is
Click here to see answer by richwmiller(17219)

Question 271971: Use binomial expansion to expand the following (2x-3y)^4
Click here to see answer by palanisamy(496)

Question 271971: Use binomial expansion to expand the following (2x-3y)^4
Click here to see answer by checkley77(12844)

Question 272429: Please help me solve
Given that y varies directly with x, write the linear function rclating the two variables.
y = 3 when x = 1/2

Click here to see answer by checkley77(12844)

Question 272429: Please help me solve
Given that y varies directly with x, write the linear function rclating the two variables.
y = 3 when x = 1/2

Click here to see answer by marno(1)

Question 273097: if X represents the first of two consecutive integers,write an expression representing the second integer
Click here to see answer by Alan3354(69443)

Question 273097: if X represents the first of two consecutive integers,write an expression representing the second integer
Click here to see answer by unlockmath(1688)

Question 273134: what is the third , fifth , and seventh term in the sequence A(n)=2n+1
Click here to see answer by mathjames(8)

Question 272931: if a is a negative number which of the following represents a postive number -3a, a\5,a-4, 2a-4
Click here to see answer by bobdabuildr(27)

Question 273969: How would you solve this equation, x^2 + 2x - 80 = 0 ?
Click here to see answer by Tobiasz(54)

Question 273969: How would you solve this equation, x^2 + 2x - 80 = 0 ?
Click here to see answer by richwmiller(17219)

Question 274053: 142. Consider the series: 80, 40, 20, 10, 5, 5/2, ____ what comes next?
1. 1/2
2. 2
3. 5/4
4. None of above
Click here to see answer by JenniferTutors(83)

Question 274056: what is the next number in the following pattern 1, 1/2, 1/4, 1/8
A. 1/10
B. 1/12
C. 1/14
D. 1/16
Click here to see answer by JenniferTutors(83)

Question 274051: consider the series :27, 24, 20, 15, 9, 2, what come next ?
A. 0.5
B. -6
C. -1
D. 0

Click here to see answer by JenniferTutors(83)

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