Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

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Question 1114196: If a, b, c are in A.P, then prove that
(i)
(ii)
(iii)
are also in A.P.
(PLEASE SOLVE ALL THE PARTS. I AM THANKFULL)

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Question 1114464:
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Question 1114490: Write out the terms of the geometric sequence that satisfies the given conditions.
a4=5, a5=15, n=5
what does a1, a2, and a3 = ?

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Question 1114819: If the sequence -1,2,5....forms the arithmetic sequence
(a)Write down the 4th term of the sequence
(b)which term of the above sequence is equal to 71

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Question 1114820: The sequence 4,6,11.....forms the quadratic sequence :
(a)Write down the 4th term of the sequence.
(b)which term of the sequence is equal to 81

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Question 1114820: The sequence 4,6,11.....forms the quadratic sequence :
(a)Write down the 4th term of the sequence.
(b)which term of the sequence is equal to 81

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Question 1114838: How do I find the rule for the nth term for this problem?
2, -4, 8, -10, 14,...
I have tried solving for an arithmetic and a geometric with no success and have tried quadratic but nothing works for me.

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Question 1115161: In a geometric sequence, the common ratio is -5. The sum of the first 3 terms is 147.What is the value of the first term in the sequence?
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Question 1115375: What's the next term (1,1,-2,4,-3,-1,0,0,0,8,2,-10,2,6)
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Question 1115414: hi what is the answer and why please, regards Raymond Fitzpatrick
176259=2
286941=4
347251=0
458217=2
525917=1
611382=

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Question 1115546: 1ln(2)+2ln(3)+3ln(4)+...+50ln(51)
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Question 1115601: I am having trouble with this problem. I am not supposed to have decimal answers.
Find the 19th term of 3/8, 1/2, 5/8
Thank you in advance.

Click here to see answer by MathLover1(20850) About Me 

Question 1115602: I am having trouble understanding this problem. I am supposed to show steps and not have a decimal answer.
-17/4 is the ___ term of 2 1/4, 2, 1 3/4 ?
Thank you in advance.

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Question 1115602: I am having trouble understanding this problem. I am supposed to show steps and not have a decimal answer.
-17/4 is the ___ term of 2 1/4, 2, 1 3/4 ?
Thank you in advance.

Click here to see answer by Alan3354(69443) About Me 

Question 1115702: I feel like a fool but why is 99-1+1=100. I thought the answer was 99.
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Question 1115758: Find the sum of the geometric series in a - c
A.2+6+18+54+162
B.1+1/2 +1/4+........
Find the sum of the arithmetic series
A.4+1-2-5.......-32
B.1+3/2 +2+ 5/2 +....+15/2

Solve the following system of linear equations by using the inverse matrix method:
{2x+9y=-1}
{4x+y=15}

Please I would really appreciate the help guys.GOD BLESS!

Click here to see answer by Alan3354(69443) About Me 
Question 1115758: Find the sum of the geometric series in a - c
A.2+6+18+54+162
B.1+1/2 +1/4+........
Find the sum of the arithmetic series
A.4+1-2-5.......-32
B.1+3/2 +2+ 5/2 +....+15/2

Solve the following system of linear equations by using the inverse matrix method:
{2x+9y=-1}
{4x+y=15}

Please I would really appreciate the help guys.GOD BLESS!

Click here to see answer by ikleyn(52788) About Me 

Question 1115797: I am not understanding this problem.
I need to show my work and no decimal answers.
Geometric
Find the 10th term of -3/4, -3/2, -3..
Thank you in advance.

Click here to see answer by Alan3354(69443) About Me 
Question 1115797: I am not understanding this problem.
I need to show my work and no decimal answers.
Geometric
Find the 10th term of -3/4, -3/2, -3..
Thank you in advance.

Click here to see answer by ikleyn(52788) About Me 

Question 1115795: Arithmetic -- No decimal answers
I am having trouble understanding this problem. I need to show my work as well.
Find the sum of -2+4+10+....+142
Thank you in advance.

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Question 1115795: Arithmetic -- No decimal answers
I am having trouble understanding this problem. I need to show my work as well.
Find the sum of -2+4+10+....+142
Thank you in advance.

Click here to see answer by josgarithmetic(39618) About Me 

Question 1115798: Geometric -- no decimal answers
Find the first four terms of the infinite geometric series if S=33/4 and R=1/3 .
Thank you in advance.

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Question 1115941: Write the first 5 terms of the sequence.
a1=2, a2=3

Click here to see answer by josgarithmetic(39618) About Me 

Question 1115944: Specify the values of x for which the given infinite geometric series has a sum. Then find the sum in terms of x.
1 + 4x + 16x2 + 64x3 + …

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Question 1115942: Write the first 5 terms of the sequence.
an=an-1∙an-2

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Question 1115940: Write the first 5 terms of the sequence.
a0=4, an=an-1∙an-2

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Question 1115943: 5. A mutual fund is an investment company that distributes shares of its own stock continuously and is obligated to repurchase the stock from the shareholders upon request. A mutual fund owns the securities of several corporations and receives dividends on the shares that it holds. These cash dividends are then paid to its shareholders, who in turn may reinvest the dividends automatically in additional shares. In mutual funds, it is hoped that a loss in one holding will be compensated for by a gain in another holding. One important advantage of these funds is that they usually choose stocks or bonds that are most likely to yield profits, reducing your chances of losing money.
A popular type of mutual fund is a money market fund, which invests only in high-yielding government and corporate short-term securities. These types of funds provide an alternative to a savings account in a bank because they usually have higher interest rates. A certificate of deposit, commonly known as a CD, is a type of money-market fund.
The mutual fund actually originated in Europe in the early part of the nineteenth century and did not become popular in the United States until the 1920s. Mutual funds experienced a period of tremendous growth after World War II.
Suppose you began making annual investments several years ago in a mutual fund in order to save for retirement. You initially invested $1000 and increased this amount by 3% per year as your salary rose. Shares of the fund initially cost $50 each and have been increasing in price by 12% each year.
a) Write a rule for the amount invested in year n.
b) Write a rule for the share price in year n at the time you invested.
c) Write a rule for the number of shares bought in year n.
d) Even though you have been investing larger amounts of money each year, your recent annual statements from your mutual fund company show that the number of shares you own has barely increased at all. Has the company made an error? Justify your answer mathematically.

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Question 1116008:
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Question 948628: In the card shop, there is a shelf with 25 cards in each row. There is a display rack with 45 cards. There are 220 cards altogether. How many rows are on the shelf?
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Question 136767: -15+-3+9+21+33+45+57+69+81+96
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Question 28030: find the mean, median, and mode of the set: 1,2,2,3,3,3,4,4,4,4
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Question 38658: write in expanded form? what does that mean?
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Question 51048: -(-2)3
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Question 54872: Hello, I could really use some help on this one. Thanks! Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. How much time did each require?
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Question 54872: Hello, I could really use some help on this one. Thanks! Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. How much time did each require?
Click here to see answer by MathTherapy(10552) About Me 

Question 79736: 1,1,2,3,5,8 That sequence is called?
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Question 80665: The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?
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Question 80665: The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?
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Question 80665: The difference of two numbers is 33. The second is 7 less than 3 times the first. What are the two numbers?
Click here to see answer by ikleyn(52788) About Me 

Question 83870: identify the common difference,d
2,4,6,8,10,...

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Question 83870: identify the common difference,d
2,4,6,8,10,...

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Question 87251: I would really appreciate any help with this problem. If i learn this one i should be able to do the others following. Write a recursive rule for the sequence. The sequence may be arithmetic, geometric, or neither. 6,10,14,18,22..
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Question 97099: what comes next in the sequence.
1,3,7,13

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Question 1116107: what number is needed to complete the pattern
66 73 13 21 52 __ 10 20

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Question 1116320: Calculate

9^563 mod907

Identify which one of the following options gives the correct solution for the above expression ?


310

520

630

493



My working:

9^563 mod 907
First I identified the exponents.
9^1 mod 907
9^2 mod 907
9^16 mod 907
9^32 mod 907
9^512 mod 907
(512+32+16+2+1=563)
9^1 mod 907=9
9^2 mod 907=81
9^16 mod 907 =669
9^32 mod 907 =410
9^512 mod 907=862
To show my working between 9^32 mod 907 and 9^512 mod 907
9^64 mod 907= 410^2 mod 907 =305
9^128 mod 907=305^2 mod 907=511
9^256 mod 907 =511^2 mod 907 = 812
9^512 mod 907= 812^2 mod 907=862
But I am not sure what is the final step....

Click here to see answer by ikleyn(52788) About Me 

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