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

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Question 1141538: The fourth term of an Arithmetic Progression (A.P) is one less than twice the second term. If the sixth term is 7, find the first term.
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Question 1141546: Find the term containing y^3 in the expansion of (sqrt 2 +y)^12
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Question 1141644: If an = 3n + 4, find the sum of the first 20 terms in the sequence.
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Question 1141723: A college savings account is constructed so that $1000 is placed in the account on January 1st of each year with a guaranteed 3% yearly return in interest, applied at the end of each year to the balance in the account. If this is repeatedly done, how much money is in the account after the $1000 is deposited at the beginning of the 19th year? Show the sum that leads to your answer as well as relevant calculations.

I get that a1 is 1000 and n is 19 but how do I find r?

Click here to see answer by MathLover1(20850) About Me 
Question 1141723: A college savings account is constructed so that $1000 is placed in the account on January 1st of each year with a guaranteed 3% yearly return in interest, applied at the end of each year to the balance in the account. If this is repeatedly done, how much money is in the account after the $1000 is deposited at the beginning of the 19th year? Show the sum that leads to your answer as well as relevant calculations.

I get that a1 is 1000 and n is 19 but how do I find r?

Click here to see answer by MathTherapy(10552) About Me 

Question 1141724: A quadratic pattern has a second term equal to 1,A third term equal to -6 and a fifth term equal to -4
1.1 calculate the second difference of this quadratic pattern
1.2 hence or otherwise, calculate the first term of the pattern

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Question 1141724: A quadratic pattern has a second term equal to 1,A third term equal to -6 and a fifth term equal to -4
1.1 calculate the second difference of this quadratic pattern
1.2 hence or otherwise, calculate the first term of the pattern

Click here to see answer by Edwin McCravy(20056) About Me 

Question 1141885: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80.
a) set up a system if equations to represent the situation.
b) find the number of quarters in the bank.

Click here to see answer by josmiceli(19441) About Me 
Question 1141885: The total value of quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would be $7.80.
a) set up a system if equations to represent the situation.
b) find the number of quarters in the bank.

Click here to see answer by josgarithmetic(39617) About Me 

Question 1141886: A G. P is such that the third term is nine times the first term, while the second term is one twenty fourth of a fifth term, find it fourth term
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Question 1141964: 3,-6,12,4,20,?
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Question 1142022: On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 4 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 57 miles with the wind, he could go only 33 miles against the wind.
What is his normal bicycling speed with no wind?

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Question 1142022: On a particular day, the wind added 4 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 4 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 57 miles with the wind, he could go only 33 miles against the wind.
What is his normal bicycling speed with no wind?

Click here to see answer by ikleyn(52787) About Me 

Question 1142261: What is the tenth term of this sequence and the next three terms
81,54,36,24,_,_,_
A10=

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Question 1142261: What is the tenth term of this sequence and the next three terms
81,54,36,24,_,_,_
A10=

Click here to see answer by greenestamps(13200) About Me 

Question 1142288: What is the next term in this series?
1,3,7,17,____

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Question 1142450: 8,5,4,9,1,7,_
What should be the answer after 7? Our subject is Mathematics in the Modern World and the lesson is about Patterns and Numbers in Nature and the World. I'm not really sure if the answer is 3 or 6😢. Please help me solve this. Thank you!

Click here to see answer by josgarithmetic(39617) About Me 
Question 1142450: 8,5,4,9,1,7,_
What should be the answer after 7? Our subject is Mathematics in the Modern World and the lesson is about Patterns and Numbers in Nature and the World. I'm not really sure if the answer is 3 or 6😢. Please help me solve this. Thank you!

Click here to see answer by math_helper(2461) About Me 

Question 1142448:
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Question 1142449: 2,5,10,17,x, 37,y, 65,z, _
I really don't have any idea of what to answer, it has letters man. Our subject is Mathematics in the Modern world and the Lesson was about Patterns and Numbers in Nature and the World.

Click here to see answer by josgarithmetic(39617) About Me 

Question 1142531: Please help me find the common difference of the sequence 1,16,81,256,625,_ So that i can calculate for the 6th term
Click here to see answer by math_helper(2461) About Me 
Question 1142531: Please help me find the common difference of the sequence 1,16,81,256,625,_ So that i can calculate for the 6th term
Click here to see answer by greenestamps(13200) About Me 

Question 1142569: the 7th term of an arithmetic sequence is 1/2 and the 14th term is
6 what is the 10th term?

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Question 1142569: the 7th term of an arithmetic sequence is 1/2 and the 14th term is
6 what is the 10th term?

Click here to see answer by Edwin McCravy(20056) About Me 
Question 1142569: the 7th term of an arithmetic sequence is 1/2 and the 14th term is
6 what is the 10th term?

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Question 1142598: Insert 4 arithmetic means between -12 and 4 ?
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Question 1142632: Please help me solve this:
Find the general term of the sequence:
1,5/2,5,17/2,13

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Question 1142632: Please help me solve this:
Find the general term of the sequence:
1,5/2,5,17/2,13

Click here to see answer by MathTherapy(10552) About Me 
Question 1142632: Please help me solve this:
Find the general term of the sequence:
1,5/2,5,17/2,13

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Question 1142631: Please help me solve this sequence: Find the general term of the sequence {{ 1, 5/2,5,17/2,13 }}
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Question 1142622: Priya earned ₹15,000 in the first month. Thereafter her salary increased by ₹1500 per
year. Her expenses are ₹13,000 during the first year and the expenses increases by
₹900 per year. How long will it take for her to save ₹20,000 per month.

Click here to see answer by Theo(13342) About Me 

Question 1142666: I am trying to determine the missing number in the pattern:
51, 57, 54, 60, _______ 63, 66
I noticed the number 3 is divisible by all the numbers. However, there is no number divisible by 3 that is between 60 and 63.
docmaine@yahoo.com

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Question 1142744: which term of the sequence (3,19,35,....) is 307?

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Question 1142751: insert 3 arithmetic means between 6 and 54
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Question 1142892: give the general term 4,-6,11,-18,30,...

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Question 1142922: Solve for x if 199 + 195 + 191 + ... + 7 + 3 = x + 1 + 5 + ... 189 + 193 + 197.
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Question 1126796: a) Find in ascending powers of x the expansion of (2-x/2)^6
b) State the first three terms in the expansion of (1+ax+bx^2)^4, if these are 1+8x+12x^2,find the values of a and B.

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Question 1142994: Please solve this sequence 1,2,3,5,16
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Question 1143022: Please someone throughly explain this question and solve it step by step so that I can understand, thank you and god bless you. :D
The terms 4x + 36, 2x + 15, and 3x - 30 are consecutive terms in an arithmetic sequence. The value of x is

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Question 144040: I have the sequence 2,5,9,14,20,27,35,44...
How can I find an explicit formula to find the nth term? How can I find the nth term if An = 324?

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Question 1143052: 3, -6, 12, 4, 20 what's the equation for this sequence and the next no.
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Question 1143158: what is the next number in the sequence below?
5,3,9,13,23

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Question 1143158: what is the next number in the sequence below?
5,3,9,13,23

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Question 1143208: 3, -6, 12, 4, 20 ?
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Question 1143233: 1.3 For an arithmetic series consisting of 15 terms Sn=2n-n^2
Determine:
(a) the first term of the sequence.
(b) the sum of the last 3 terms
Please help me please

Click here to see answer by greenestamps(13200) 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