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 891203: Hilda is making a rectangular banner. The length of the banner is 5 feet longer than the width. Jenny is decorating a square banner. The sides of Jenny's square banner are equal to the width of Hilda's banner. What is the ratio of the area of Hilda's banner to the area of Jenny's banner? Use this ratio to find the ratio of the areas if the width of Hilda's banner is 3 feet.

Click here to see answer by josgarithmetic(39617)

Question 891200: Find the LCM of c2 + 5c + 6 and 3c2 + 21c + 36
Click here to see answer by Fombitz(32388)

Question 891275: what is the position to term rule for 9,7,5,3,1,-1,-3
Click here to see answer by Edwin McCravy(20056)

Question 891254: 1,2,4,8,16,22,24,28...
where each number is the sum of the previous number and its final digit. How many numbers in the sequence are less than 1000?
Click here to see answer by Edwin McCravy(20056)

Question 891345: In the following equation, A, B, C, and D are all positive integers such that A has 4 factors, B has 6 factors, and D has 8 factors. What is the smallest possible sum of A, B, C, and D, if (A�B)/C = D ?
Click here to see answer by richard1234(7193)

Question 891404: Q:The fourth term of the geometric progression is 8 and the sum of first 6 terms of the series is 63. Find the first term and the common difference?
Click here to see answer by richwmiller(17219)

Question 891467: Find two numbers with sum 82 and difference 30?
Click here to see answer by Fombitz(32388)

Question 891573: Can you please help me solve this question? Many of the terms have a # or a letter with a # or letter written just below it. I will use "sub" showing what is written that is lowered. It's like the opposite location from an exponent.
List the first six terms of the sequence defined recursively by (1) z(sub 1)=0, z(sub 2)=1, z (sub 3)=2, and (2) for m>=4, z(sub m)=z (sub m-1) + 2z(sub m-2) + 3z (sub m-3).
I sure hope that doesn't sound confusing. Any help you can give would be much appreciated. Thank you.
Click here to see answer by KMST(5328)

Question 891655: Q. Find the wrong number in the series
8, 17, 37, 79, 165, 338
Click here to see answer by fcabanski(1391)

Question 891685: A brick wall is built with bottom row having 50 bricks. Each row on top of that is one less. The next is 49, then 48 and so on continuing on until the top row is just 1 brick. A) How can I write the total # of bricks as a summation?
Here's what I know. I know the answer is 1275 bricks. I know d=1. I tried sn=((n)(2a(sub1) + (n-1) d)) / 2. I tried solving with 50 plugged in for n and 1 in for 2a(sub1), and vice versa. I am 25 away from the correct answer. Just not sure of the placement of my numbers.
Thank you for any help you can give.
Click here to see answer by Fombitz(32388)

Question 891696: Please help me complete this number sequence.
48, 24, 60, 30, 30, ___, 20, 10
Thanks.
Click here to see answer by robertb(5830)

Question 891682: Hello. Hoping you can help me answer this question. A) write geometric series -9/2+3/2-1/2+1/6...+1/39366 in summation notation. B)using the formula for the sum of an geometric series, compute the sum.
Here's what I know. The numerator is multiplied by 1/3 to get from each term to the next. The denominator decreases by 1 when comparing n=term #, n=1 to denom in -9/2, 2-1=1, n=2 in 3/2, 2-2=0 and so on. I see the pattern, just not sure how to write it. Also, when writing it in sn, I know my bottom starting amount will be n=1
Any help you can give would be appreciated. Thank you.
Click here to see answer by Fombitz(32388)

Question 891695: The sum of first 20 and 50 terms of an AP is 420 and 2550. Find the eleventh term of a GP whose first term is the same as the AP and the common ratio is equal tithe common difference of the AP ?
Click here to see answer by robertb(5830)

Question 891699: 1,3,6,10.15, ... , n?
Click here to see answer by robertb(5830)

Question 891699: 1,3,6,10.15, ... , n?
Click here to see answer by richwmiller(17219)

Question 891783: The sum of how many terms of the series 3,-6,12, ....will be 513?
Click here to see answer by josgarithmetic(39617)

Question 891829: the sum of the finite arithmetic series 2+4+6+8...+70 is
Click here to see answer by LinnW(1048)

Question 892087: Find the sum of
(1+2+3....+x) + (2+3+4....+x) + (3+4+5....+x) + ...................... till n terms where n
Click here to see answer by robertb(5830)

Question 892169: the second term of an arithmetic sequence is 7, the sum of the first four terms in the arithmetic sequence is 12, find the first term and the common difference

Click here to see answer by josgarithmetic(39617)

Question 892289: A line segment was halved and the two hence formed line segments were further halved and so on.
Write an expression that represents the number of line segments obtained when halved n times starting from n=1.
Is it possible to obtain 144 line segments in this process?

Click here to see answer by josgarithmetic(39617)

Question 892335: How do I determine the next term in the sequence 2;4;8;16;32;
Click here to see answer by Fombitz(32388)

Question 892331: 1 3 7 9 11 15 17 21 37 41 44 How to get a next two number in this series?
Click here to see answer by Edwin McCravy(20056)

Question 892345: What is the next number in the line 15, 6 , 18 , 10, 30, 23, 69, ... ?
The possible answer are : 58, 60, 63, 65, 79
This is a test on the web but i don't find the right one, i'm asking myself if this test is right.
Click here to see answer by ankor@dixie-net.com(22740)

Question 892466: the sum of 9 numbers is 353. if the average of four of the numbers is 32, what is the average of the remaining numbers?
Click here to see answer by richwmiller(17219)

Question 892466: the sum of 9 numbers is 353. if the average of four of the numbers is 32, what is the average of the remaining numbers?
Click here to see answer by stanbon(75887)

Question 892466: the sum of 9 numbers is 353. if the average of four of the numbers is 32, what is the average of the remaining numbers?
Click here to see answer by josgarithmetic(39617)

Question 892466: the sum of 9 numbers is 353. if the average of four of the numbers is 32, what is the average of the remaining numbers?
Click here to see answer by MathTherapy(10552)

Question 892438: Describe the following pattern: (-1)1=? ;(-1)-2=? ;(-1)-3=? ;(-1)-4=?. Determine what (-1)-100 would be. Justify your thinking. The numbers outside the parentheses are exponents.
Click here to see answer by Fombitz(32388)

Question 892520: In an AP, the sum of the first three terms is 18, and the sum of the squares of these terms is 126. Find the three terms.

Click here to see answer by richwmiller(17219)

Question 892571: Find the next two
numbers in the
sequence. What is
the rule?

100, 25, 50, 12.5, 25,
____, ____
Click here to see answer by richwmiller(17219)

Question 892599: Find the sum of the first 100 positive even integers.
2+4+6+8+....+200

Click here to see answer by josgarithmetic(39617)

Question 892724: The sum of the terms of a finite arithmetic series is 624.
If the sum of the 1st term and last term is 48,
how many terms are there in the sequence?

Click here to see answer by robertb(5830)

Question 892831: What are the missing numbers for this problem? 120,60,180,90, _,_,405

Click here to see answer by AnlytcPhil(1806)

Question 892532: sn problem; above greek symbol is k on the bottom is n=0. Directly next to it is n^2=(k(k+1)(2k+1))/6 check that its correct for k=1,2, and 3.
B.) Use the same formula to compute the value of m=0 top 5 (2m^3+3m-4)
Thank you.
Click here to see answer by richard1234(7193)

Question 893052: if the sum of first n terms of the series 5,9,13,17,....is 275 then find n.

Click here to see answer by josgarithmetic(39617)

Question 893319: what is 75 term of sequence 4,7,10
Click here to see answer by MathLover1(20850)

Question 893368: Write the general term for the following sequences:
1. 1/2, 1/3, 1/4, 1/5, ...
2. 1, 8, 27, 64, ...
3. 7, 7, 7, 7, ...
4. 1/11, 2/12, 3/13, 4/14, ...
5. 9, 99, 999, ...
6. 1, 1, 2, 3, 5, 8, ...

Click here to see answer by josgarithmetic(39617)

Question 893401: In an arithmetic sequence, the sum of the first three terms is 18 and the sum of the squares of these terms is 126. Find the terms

Click here to see answer by Theo(13342)

Question 893507: what are the next two terms in this sequence;
1/8, 2/7, 1/2, 4/5
Click here to see answer by richwmiller(17219)

Question 893579: Write the general term of the sequence: 9, 99, 999, ...
Click here to see answer by josgarithmetic(39617)

Question 893604: the sum of the number is 103. what is the number

Click here to see answer by Alan3354(69443)

Question 893591: what should be added to 71 to make the sum 101?

Click here to see answer by Jynald-(6)

Question 893723: how can I find the next two numbers in this series:
32,-48,72,-108

Click here to see answer by josgarithmetic(39617)

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