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 852685: if 2 terms in AP series are 4 and 9 in ratio 1:3 .. then find D and A??
Click here to see answer by richwmiller(17219)

Question 846804: Suppose that n represents a positive even integer. What expression represents the next even integer? the next odd integer? I am thinking of three consecutive even integers, whose sum is 204. What are they?
(continued) Find three consecutive odd numbers whose sum is 117. Find two ways to do this.

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Question 846294: The 3rd term of an arithmetic sequence is 24 times less than term 7,the sum of term 5 and term 10 is 8.
1.calculate the first three terms of the sequence

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Question 844124: the number 105 can be expressed as a sum of two or more consecutive positive integers in seven different ways.
One such sequence begins with 12- i.e- 12+13+14+15+16+17+18=105 What do the other six sequences begin with?
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Question 844216: if AM between 2 no's is 5 and their Gm is 4 then the HM will be
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Question 844214: if a,8,b are in AP and a,4,b are in GP a,x,b are in HP then x =
Click here to see answer by richwmiller(17219)

Question 845306: find first term and common ratio of a geometric sequences given sixth term 486 and third term 18

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Question 852926: I need explanation:
The product of four consecutive natural numbers is 255024. Find these numbers.

Click here to see answer by Alan3354(69443)

Question 852942: What are the two successive numbers immediately after 57??
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Question 852976: 2x^2/2x^3-18x + 15/5x-15
Click here to see answer by ewatrrr(24785)

Question 852988: 1/a-b + 1/b-a
How does this come out to 0?
Click here to see answer by stanbon(75887)

Question 852988: 1/a-b + 1/b-a
How does this come out to 0?
Click here to see answer by ewatrrr(24785)

Question 853079: 1/a-b + 1/b-a
I'm confused, why is the answer 0? Could you answer the question in a specific step by step process please, I'd really appreciate it.
Click here to see answer by ankor@dixie-net.com(22740)

Question 853085: 1/a-b + 1/b-a
I'm confused, why is the answer 0? Could you answer the question in a specific step by step process please, I'd really appreciate it.
Click here to see answer by Alan3354(69443)

Question 849049: The first,third and eight term of an arithmetic sequence form the first three terms of a geometric sequence.
If the term is 4, find the common difference of the arithmetic sequence.
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Question 853096: the third term of an arithmetic sequence is 9. The sum of the next two terms is -18. Find the first two terms of the sequence; write a sequence formula and an explicit formula
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Question 851540: How to find the terms of a gp with the sum
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Question 852756: 39,42,46,50
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Question 849064: Find the 4th term of the sequence an = 1000 (0.1)^n-1
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Question 853249: Is the sequence arithmetic? If so, identify the common difference. 15, 22, 35, 46,...
Answers (a)yes:7, (b)yes:-7, (c)no (d)yes:13
Click here to see answer by ramkikk66(644)

Question 853253: The numbers of seats in the first 12 rows of a high school auditorium form an arithmetic sequence. The first row has nine seats. The second row has 11 seats.
a). Write a recursive formula to represent the sequence.
b). Write an explicit formula to represent the sequence.
c). How many seats are in the 12th row?
Click here to see answer by ramkikk66(644)

Question 853255: Robin bought a computer for $1,250. It will depreciate, or decrease in value, by 10% each year that she owns it.
a). Is the sequence formed by the value at the beginning of each year arithmetic, geometric, or neither? Explain.
b). Write an explicit formula to represent the sequence.
c). Find the value of the computer at the beginning of the 6th year.
Click here to see answer by richwmiller(17219)

Question 853269: 1Is the sequence geometric? If so, identify the common ratio.
1/4, 3/16, 9/64, 27/256, 81/1024.
a) yes: 1/3
b) yes: 3/4
c) not geometric
d) yes: 2/9

Click here to see answer by fcabanski(1391)

Question 853270: Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series 3+10+17+24+...
a). Use summation notation to write the series. Explain what the numbers in the summation notation represent in this situation and how you found the expression used in the summation.
b). Find the total number of beads in the necklace. Explain your method for finding the total number of beads.
Click here to see answer by mananth(16946)

Question 853268: Write an explicit definition for the sequence -4, 1, 6, 11,...
answer a is An=-4+5(n+1)
answer b is An=-4+5(n-1)
answer c is An=-4+(n-1)
answer d is An=-4+5n
Click here to see answer by josgarithmetic(39617)

Question 853272: What is the 10th term of the sequence 64, 16, 4,...?
a. 1/2024
b. 1/256
c. 1/4096
d. 1/496
Click here to see answer by fcabanski(1391)

Question 853286: Use summation notation to write the series 2.2+8.8+15.4+... for 5 terms.
Click here to see answer by Edwin McCravy(20056)

Question 853285: Does the infinite geometric series diverge or converge? Explain.
2+6+18+54+...
a - It diverges: it does not have a sum.
b - It converges: it does not have a sum
c - It diverges: it has a sum
d - It converges: it has a sum
Click here to see answer by Edwin McCravy(20056)

Question 853296: Please help me find the general term for the following sequence: -14 -15 -12 -5 6
I got the first difference (3 7 11) and the second ( 4 ) but can't get a general formula! Please help!
Click here to see answer by Edwin McCravy(20056)

Question 853282: A rubber ball dropped on a hard surface takes a sequence of bounces, each on 2/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled after it hits the surface the fifth time? Be sure to account for both drop and rebound differences.
a - 22 12/25feet
b - 32 124/125feet
c - 25 124/125feet
d - 22 124/125feet
Click here to see answer by mananth(16946)

Question 853278: What is the sum of the first 10 terms of the sequence defined by An=4n-3?
a. 37
b. 190
c. 380
d. 384
Click here to see answer by richwmiller(17219)

Question 853273: What is the sum of the finite arithmetic series?
(-5)+0+5+10+...+65
a. 900
b. 455
c. 450
d. 445
Click here to see answer by richwmiller(17219)

Question 849604: . A person is entitled to receive an annual payment which for each year is less by one tenth of what it was for the year before. If the first payment is 100. Then, find the maximum possible payment which he can receive, however long he may live?
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Question 846479: The shortest side of a triangle with perimeter 35cm is 5cm.calculate the length of the other two sides if they are in a geometric progression
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Question 853436: what is the common ratio of this geometric sequence:
1/x, 1/x2, 1/x3
Click here to see answer by chndnbl(31)

Question 853476: For part (a), find the sum of the first n terms of the geometric
series.
60. 1 + 4 + 16 + 64 + . . .
a. n = 14
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Question 844447: 16, 24, 32, 44, 60, 82, . . .
Find the recursive formula
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Question 853590: What is the sum of the infinite geometric series?
(-15)+ 0+ 15 +30+.....+195
Please show me step by step, thank you in advance!
Click here to see answer by richwmiller(17219)

Question 853586: What is a possible term for the geometric sequence? 37, ___, 925
Could somebody show me step by step please and thank you for your help in advance
Click here to see answer by richwmiller(17219)

Question 853737: Find the first term and the common difference of the arithmetic sequence whose 5th term is 7 and 13th term is 39.
Click here to see answer by richwmiller(17219)

Question 853736: Find the first term and the common difference of the arithmetic sequence whose 5th term is 7 and 13th term is 39.
Click here to see answer by richwmiller(17219)

Question 844215: if AM between 2 no's is 5 and their Gm is 4 then the HM will be
Click here to see answer by richwmiller(17219)

Question 844511: If 5/3 and 20 are the first and last terms respectively,of a geometric sequence,determine the value(s) of the fifth term if there are seven terms in the sequence
Click here to see answer by richwmiller(17219)

Question 842381: The common ratio of a geometric series is 1/3 and the sum of the first 5 terms is 121. What is the value of the first term?
Click here to see answer by richwmiller(17219)

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