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

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Question 1169395: In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th terms.
Thanks for your help.
Click here to see answer by MathLover1(20850)

Question 1169395: In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th terms.
Thanks for your help.
Click here to see answer by math_helper(2461)

Question 1169395: In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th terms.
Thanks for your help.
Click here to see answer by ikleyn(52787)

Question 1169395: In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th terms.
Thanks for your help.
Click here to see answer by MathTherapy(10552)

Question 1169395: In this arithmetic sequence wee are given that S1=9 AND S2=20
What is the 4th terms.
Thanks for your help.
Click here to see answer by greenestamps(13200)

Question 1169339: use the reminder theorem to find the remainder when the given polynomial is divided by each polynomial
4×3-×2+3×-2÷×+1
Click here to see answer by The Troll Kid(22)

Question 1169419: pls help me to find the number pattern
1. 2,4,18 _,530,_
2. 1,4,_,5,_,0
3. 1,9,_,260,1590,_
Click here to see answer by ikleyn(52787)

Question 1169628: I need help on Write the next three terms in the sequence. Use a comma to separate the numbers.
-16, -7, 2, 11, ...
Click here to see answer by josgarithmetic(39617)

Question 1169808: a pine sapling was 3 meters tall when it was first planted. in its first year, it grew 1 meter. in each successive year, it grew 75% of the previous year's growth. if it continues to grow in this manner, what is the maximum height the tree can grow to? ( hint: remember to add in the original height of the seedling.)

Click here to see answer by greenestamps(13200)

Question 1170239: insert eight arithmetic mean between 26 and -10

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Question 1170252: The sequence {an} is defined recursively as follows: a1 = 6 and an+1 = 3. Find an explicit formula for an (that is, in terms of n), and prove your formula by mathematical induction.
Click here to see answer by ikleyn(52787)

Question 1170329: The 6th term of Ap is 35 and the 13th term is 77. find the 20th term
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Question 1170344: Given an arithmetic sequence, 2,−1,−4,−7,...
Firstly, Find the common difference, then, find the 120thterm, and lastly, find which term is −595.

Click here to see answer by Boreal(15235)

Question 1170402: Roll of insulation are selected so that each layer after the first has 6 fewer rolls than the previous layer. How many total rolls of insulation are there of there are 5 layers in total?
Click here to see answer by greenestamps(13200)

Question 1170423: Why is the sequence between these numbers please and thanks 8 10 32 34

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Question 1170423: Why is the sequence between these numbers please and thanks 8 10 32 34

Click here to see answer by ikleyn(52787)

Question 1170453: If S1=0.7 and S2=2.1, in a geometric series, determine the sum of the first 12 terms In the series
Click here to see answer by Boreal(15235)

Question 1170436: the 5th term in a geometric progression is 9 times the 3rd term and the sum of the 6th and 7th terms is 1944. determine the common ratio, the first term the sum of the 4th to 10th terms inclusive

Click here to see answer by Boreal(15235)

Question 1170500: Write the general terms of the following sequence:
𝑌=(0,9,26,65,.........)
Click here to see answer by Edwin McCravy(20056)

Question 1170526: Why is the sequence between these numbers please and thanks 8 10 32 34
Click here to see answer by ikleyn(52787)

Question 1170588: For the following limit : 𝐥𝐢𝐦(√𝒏/(𝒏+𝟏))=𝟎.
Find 𝐾(∊)when ∊= 0.0001 and verify your answer.
Click here to see answer by math_helper(2461)

Question 1170615: what is the seventh term of geometric sequence of 1, -3, 9, -27
Click here to see answer by Boreal(15235)

Question 1149395: What is the sum of the two missing numbers in the sequence 4,3,3,2,3,3,7,7,2,_,_,?
Click here to see answer by akumpo(8)

Question 1170590: Prove the following limits using
(i)The definition(ii) Corollary of Archimedean Property (iii)Theorem 3.1.10
(a) 𝐥𝐢𝐦(𝟐𝒏+𝟓)/(𝟔𝒏−𝟑)=𝟏/𝟑(b) 𝐥𝐢𝐦(𝒏^2 +𝟏)/(𝟐𝒏^𝟐)=𝟏/𝟐
Click here to see answer by Solver92311(821)

Question 1170792: Hence,Find a and b if for all positive integers n.
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Question 1170890: Hi I want to know what number comes next in this number or which method didi they use in this numbers. 12,38,40,3,9,18,37
Click here to see answer by ikleyn(52787)

Question 1171020: 4,1,3,6,5,3,5,7,9,4,7,1,6,1,7,3
Click here to see answer by ikleyn(52787)

Question 1171042: Determine whether the following set of ordered pairs is a function. Justify your answer.
{(9, 3), (2, -2), (-4, 7), (-4, 5)}
Click here to see answer by josgarithmetic(39617)

Question 1171042: Determine whether the following set of ordered pairs is a function. Justify your answer.
{(9, 3), (2, -2), (-4, 7), (-4, 5)}
Click here to see answer by MathLover1(20850)

Question 1171185: The 16th term of an ap is 93, given that its common difference is 6. find the first term and 28th term
Click here to see answer by ikleyn(52787)

Question 1171273: In the continuation of this array of positive integers, in which column is the number 12000?
A) 99
B) 100
C) 101
D) 102
E) 103
https://ibb.co/KG8z40Y
Click here to see answer by MathLover1(20850)

Question 1171297: Find the sum of the first 21 terms of the progression -10, -8, -6, .....
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Question 1171554: 3, -6,, 12, 4, 20 ....
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Question 1171677: Question: The sum of 40 terms of a certain arithmetic sequence is 430, while the sum of 60 terms is 945. Determine the nth term of the arithmetic sequence.
What I did so far: a1 + 39d = 430 ……….Eq(1)
a1 + 59d = 945 ……… Eq (2)
Solving for d: 20d = 515 and d = 25.75
Therefore the nth term of the arithmetic sequence= a1 +(n - 1)25.75
The different answer given in the book is: (n + 1)/2
What am I missing?
Please help.
Thanks
PLEASE FORGET THIS QUESTION: I USED THE LAST TERM FORMULA AND EQUATED THAT TO SUM!

Click here to see answer by math_tutor2020(3817)

Question 1171691: what is the next three terms in the following sequence
2, -8, -18, -28,
Click here to see answer by ikleyn(52787)

Question 1171731: Question: In a set of four numbers, the first three are in a geometric sequence and the last three are in an arithmetic sequence with a common difference of 6. If the first number is the same as the fourth, find the four numbers.
What I have come up with so far:
GP: a, ar, ar^2
AP ar, ar+6, ar+12
a = ar + 12
ar^2 = ar + 6
I am stuck
Not able to generate a system of equations to solve for a or r.
Please help.
Thanks
Click here to see answer by ikleyn(52787)

Question 1171893: what is the missing number? 7.3 8.1 8.5 8.9
Click here to see answer by math_helper(2461)

Question 1171905: Find the common difference for the following sequence and fill in the missing terms show all calculations -12,__,10,__,32,43
Click here to see answer by Alan3354(69443)

Question 1171967: The square root of the sum of a square number increased by 7 added to the number that is equal
to 7. What would be the number?
Click here to see answer by ikleyn(52787)

Question 1172132: What is the hundredth term of the sequence with a sub one equals 222 and d equals -5?
Click here to see answer by Edwin McCravy(20056)

Question 1172317: If n = (p1 )^α1 .(p2)^α2.(p3)^α3 .(p4)^α4 .....(pr)^αr where p1 , p2,
p3 , ...., pr are distinct prime numbers then prove the following result:
d(n) = infinite product of (αi + 1) [Note: Here ^ means power]
Click here to see answer by ikleyn(52787)

Question 1172323: What is the nth term of the sequence: 5,5,35,65,275
Click here to see answer by ikleyn(52787)

Question 1172321: The integers 1, 2, 3, ...., 40 are written on white board. An operation is then repeated 39 times. In each repetition any two numbers say a and b currently on white board are erased and new number a + b -1 is written. What will be the number left on white board at the end?
Click here to see answer by Edwin McCravy(20056)

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