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 567791: sarah can shovel her driveway in 35 minutes. John can do the same job in 30 mintues. If they work together how many minutes would it take to shovel the driveway.
I got as far at t/30+t/35=1
Click here to see answer by Earlsdon(6294)

Question 567832: the 15th term in an arithmetic sequence is 43 and the sum of the first 15 terms of the series is 120. Determine the first three terms of the series
Click here to see answer by solver91311(24713)

Question 568043: please explain how to find only thee sum of the odd numbers in sigma notation n=1-35
Click here to see answer by KMST(5328)

Question 568401: Please help me in solving this arithmetic sequence.: The 21st term of the arithmetic sequence is -48, and the 33rd term is -84. Find the 101st term.
Click here to see answer by htmentor(1343)

Question 568527: not getting the understanding of these problems and they need to be self explanatory to me.
8,11,14,17,20
1,16,81,256,625
5,15,45,135,405
2,7,12,17,22
1,1/2,1/4,1/8,1/16
Click here to see answer by jim_thompson5910(35256)

Question 568427: How many terms are there in this sequence: 12,15,18,21.......267
Click here to see answer by richard1234(7193)

Question 568967: write the first three terms of an arithmetic sequence if the fourth term is 10 and d=-3.
Click here to see answer by scott8148(6628)

Question 569333: the equation is 1+2+4+8..., n-6 i know the answer is 63 but idk how to get the answer and what formulas to use
Click here to see answer by solver91311(24713)

Question 570125: I am having issues with determining a of n when the only given are two terms from an arithmetic series. The two terms given are a of 8= 75 and a of 20= 75. What would a of n be??
Click here to see answer by htmentor(1343)

Question 570216: The sum of x and 5 is 16.
Click here to see answer by jim_thompson5910(35256)

Question 570818:
2. Which number should come next in the series?
1,4,9,16,25
27
34
36
45
I don't know
Click here to see answer by KMST(5328)

Question 570772: In the figure below, line m is parallel to line n, and line t is a transversal crossing
both m and n. Which of the following lists has 3 angles that are all equal in measure?
A. ∠a, ∠b, ∠d
B. ∠a, ∠c, ∠d
C. ∠a, ∠c, ∠e
D. ∠b, ∠c, ∠d
E. ∠b, ∠c, ∠e
Click here to see answer by richard1234(7193)

Question 571200: what is the 11th term of the geometric sequence 81,-27,9?
Click here to see answer by Theo(13342)

Question 571213: geometric mean between 99 and 44
Click here to see answer by mrjunecarlo1095@ymail.com(10)

Question 571213: geometric mean between 99 and 44
Click here to see answer by Theo(13342)

Question 571989: IN A PILE OF LOGS, EACH LAYER CONTAINS ONE MORE LOG THAN THE LAYER ABOVE,IN THE TOP LAYER CONTAINS JUST ONE LOG. IF THERE ARE 105 LOGS IN THE PILE, HOW MANY LAYERS ARE THERE?
Click here to see answer by htmentor(1343)

Question 572482: 1(1!) + 2(2!) + 3(3!) + . . . + n(n!).
Find the sum of this series if n = 15.
Click here to see answer by richard1234(7193)

Question 572645: Use the Method of Finite Differences to find a function for the following sequences. 2.5, 6, 13.5, 25
Click here to see answer by Edwin McCravy(20056)

Question 572590: find the first 3 terms of a geometric progression whose sum is 42 and whose product is 512
Click here to see answer by htmentor(1343)

Question 573170: the sum of the arithmetic series is equal to the product of these two quantities. true or false?

Click here to see answer by solver91311(24713)

Question 573364: What is the Nth equation of the following pattern?
Figure 1; 3 tiles
Figure 2; 5 tiles
figure 3; 7 tiles etc.
(and I know how the pattern grows, I just need to know what the equation is)
Click here to see answer by scott8148(6628)

Question 573745: For a given map, two-thirds of an inch represents 80 miles. Two cities are 200 miles apart. How far apart are they on the map?
Click here to see answer by checkley79(3341)

Question 574037: How many terms are there in a geometric sequence if 6 is the first term, 1/2 is the common ratio and 3/64 is the last term?
Click here to see answer by reviewermath(1029)

Question 574501: 1+3+5+7+ . . . +99+101 = (?) Please show me the steps.
Click here to see answer by reviewermath(1029)

Question 574587: Find the nth term of the sequence
1 2 5 10...

Click here to see answer by stanbon(75887)

Question 574584: Can someone plz help me. plz show me how to work this problem. adding the polynomials.
(1/8x^2 -1/4x -3/8) + (-1/2x^2 -1/4x -1/2)
Click here to see answer by stanbon(75887)

Question 574659: List the first three terms of an arithmatic sequence with a first term of 6 and a twentieth term of 63
Click here to see answer by bucky(2189)

Question 574789: The sum of the first three terms of a geometric series is 14 and the product of the first three terms of this series is 64.
1. So determine the ratio?
2.Show that there are two different series that satisfy the above conditions.

Click here to see answer by richard1234(7193)

Question 574479: Find the limits of the following sequence.
{2/4n+1}
Click here to see answer by richard1234(7193)

Question 575136: The ninth term of the arithmetic sequence is 1/6 ; the sixteenth term is 2 �. Find the first term.
Click here to see answer by chana(69)

Question 576626: Find two sets of numbers whose some is 20 and whose product is 96
Click here to see answer by Alan3354(69443)

Question 577453: Find the eighth term of a sequence that has a first term of 12 and a common difference of 3. I don't get this at all.
Click here to see answer by stanbon(75887)

Question 577583: 1. If Carla can drive 400 miles on 28 gallons of gas, how many gallons of gas will she need to travel 1000 miles?
Click here to see answer by jim_thompson5910(35256)

Question 577591: Kathy stood on the middle rung of a ladder. She climbed up 5, down 3, up 8, and up 4 more to get to the top of the ladder. How many rungs are there in this ladder? I tried dividing but I am not real sure how to solve this.
Click here to see answer by ankor@dixie-net.com(22740)

Question 577920: How many terms are in the geometric sequence 8, 24, 72...648?
Click here to see answer by stanbon(75887)

Question 577920: How many terms are in the geometric sequence 8, 24, 72...648?
Click here to see answer by dfrazzetto(283)

Question 577782: In a three digit number , the hundreds digit , the tens digit and the units digit are in descending order and in Arithmetic progression . Each digit of the number is multiplied by the sum of the other 2 digits . The sum of all such results is A. B is the product of the tens digit and the sum of all the digits and A = (4/3)B . Find the number of such numbers ..

Options available are
a)4 b)3 c)2 d) More than 4
Click here to see answer by Edwin McCravy(20056)

Question 578370: Use the Maclaurin series of f(x) = e^x to verify that d/dx e^x = e^x.
Thank you!
Click here to see answer by Tatiana_Stebko(1539)

Question 578597: Does the number always have to be an even number each time to get a common difference in a arithmetic sequence?
Click here to see answer by KMST(5328)

Question 578862: Here is the sequence : 1/3 ; 1 ; 1/9 ; 4 ; 1/27 ; 7 ; 1/81;...
H e l p m e f i n d t h e n e x t t h r e e t e r m s i n t h e s e q u e n c e .
Click here to see answer by scott8148(6628)

Question 579908: Determine if the following series are convergent of divergent. If the series is geometric find the sum as well:
[(-1)^n +1] / sqr n (NOTE: +1 is separated from ^n)
at n =1 to infinity

Thank you so much!

Click here to see answer by KMST(5328)

Question 579910: Determine if the following series are convergent of divergent. If the series is geometric find the sum as well:
[cos(n*pi/3)] / n factorial
at n =1 to infinity

Thank you so much!

Click here to see answer by KMST(5328)

Question 579911: Find the limits of the sequences.
an= cos(n*pi /2)
Thank you so much!
Click here to see answer by KMST(5328)

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