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

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Question 1044383: if (x,y,12) is decreasing geometric sequence and (x,y,9) is arthemetic sequence then..evaluate the value of x,y and find Gn
Click here to see answer by ikleyn(52787)

Question 1044391: How many terms are in the following sequence?
9,19,29,...,139

Click here to see answer by Alan3354(69443)

Question 1044339: a new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a side. if the process id continued until there are already six squares, find the sum of the areas of all squares in square inches.
Click here to see answer by robertb(5830)

Question 995412: How far can you run on a 100m ground?
Click here to see answer by karks (1)

Question 1044646: what is the missing number in this sequence ?
(7,4), (4,1), (0,-3), (-5,-8), (9.5,__)
Click here to see answer by josgarithmetic(39617)

Question 1044652: What is the missing number in the sequence ?
64, -16, 4, -1, ___
Click here to see answer by josgarithmetic(39617)

Question 1044680: find the sequence and the series of {1+2+3+4...n}
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Question 1044680: find the sequence and the series of {1+2+3+4...n}
Click here to see answer by ikleyn(52787)

Question 1044698: Find the sum of the terms of a geometric sequence where the first term is 4, the last term is 324, and the common ratio is 3.
U
Click here to see answer by MathLover1(20850)

Question 1044698: Find the sum of the terms of a geometric sequence where the first term is 4, the last term is 324, and the common ratio is 3.
U
Click here to see answer by ikleyn(52787)

Question 1044781: The seventh term of an arithmetic sequence is 1/2 and the 14th term is 6. What is the tenth term?
Click here to see answer by Cromlix(4381)

Question 1044781: The seventh term of an arithmetic sequence is 1/2 and the 14th term is 6. What is the tenth term?
Click here to see answer by advanced_Learner(501)

Question 1044785: The first three terms of an arithmetic sequence are -12, -4, and 4. Which term is 212 ?
Click here to see answer by Alan3354(69443)

Question 1044785: The first three terms of an arithmetic sequence are -12, -4, and 4. Which term is 212 ?
Click here to see answer by ikleyn(52787)

Question 1044785: The first three terms of an arithmetic sequence are -12, -4, and 4. Which term is 212 ?
Click here to see answer by MathTherapy(10552)

Question 1044891: 5,9,25,91,414,2282.6
Click here to see answer by ikleyn(52787)

Question 1044947: 3408<3 []30 <3540 what is the digits can replace each empty box
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Question 1044947: 3408<3 []30 <3540 what is the digits can replace each empty box
Click here to see answer by MathTherapy(10552)

Question 1045000: Two elements of a sequence are 3 and 13.
(a) Write down the first few terms of at least four sequences having 3 and 13 as two of its elements.
(b) Find the 25th element in each of your sequences.
(c) Find the general term of each of your sequences if you can.
Click here to see answer by Edwin McCravy(20056)

Question 1045437: a + b = -8
Click here to see answer by Alan3354(69443)

Question 1045441: How do I find the general term of the arithmetic
sequence a19= 150, d=9, without the first term?
Click here to see answer by Edwin McCravy(20056)

Question 1045463: 52 53 94 46

Click here to see answer by ikleyn(52787)

Question 1045846: what number would come next in this sequence?
3, -6, 12, 4, 20
Answers 13,14, 6, or 16
Click here to see answer by ikleyn(52787)

Question 1045846: what number would come next in this sequence?
3, -6, 12, 4, 20
Answers 13,14, 6, or 16
Click here to see answer by MathLover1(20850)

Question 1046020: This is a question my teacher assigned if we want to do, it is extra, but I would like to learn more and this is a great problem. I cannot understand it no matter how hard I try. Please explain fully and how you got your answer.

For any positive integer, find the sum of the squares of its digits. If the result is 1, you�re done. Otherwise, find the sum of the squares of the digits of the result. Continue this process until the result is 1, in which case we call the original integer a happy number, or until there is a repeated result, which leads to an endless loop, in which case we call the original integer an unhappy number. For example, consider 13 and 85.

13 is a happy number since
12 + 32 = 1 + 9 = 10,
12 + 02 = 1 + 0 = 1.
85 is an unhappy number since
82 + 52 = 64 + 25 = 89,
82 + 92 = 64 + 81 = 145,
12 + 42 + 52 = 1 + 16 + 25 = 42,
42 + 22 = 16 + 4 = 20,
22 + 02 = 4, 42 = 16,
12 + 62 = 1 + 36 = 37,
32 + 72 = 9 + 49 = 58,
52 + 82 = 25 + 64 = 89, which is a repeated result.
What is the least unhappy number?

What is the least prime number that is a happy number?

What is the least integer greater than 1 that, when multiplied by any happy number, yields another happy number?
Click here to see answer by KMST(5328)

Question 1046272: The ratio between the sum of 'n' terms of two arithmetical progressions is (7n+1):(4n+27). Find the ratio of their eleventh term.
Ans: 148/111
Click here to see answer by t0hierry(194)

Question 1046326: find the sum of the G.P 1 + 3 + 9 + 27 + ------- + 729?
Click here to see answer by Boreal(15235)

Question 1046326: find the sum of the G.P 1 + 3 + 9 + 27 + ------- + 729?
Click here to see answer by ikleyn(52787)

Question 1046578: Insert 5 Geometric means between 32 and 1/2.
Click here to see answer by robertb(5830)

Question 1046578: Insert 5 Geometric means between 32 and 1/2.
Click here to see answer by Edwin McCravy(20056)

Question 1046683: what would be the formula for 1/2,1,2,4,8. pattern
Click here to see answer by ikleyn(52787)

Question 1046683: what would be the formula for 1/2,1,2,4,8. pattern
Click here to see answer by Edwin McCravy(20056)

Question 1046851: Hi I need help on these questions.
"Determine the relationships and express them using variables."
Input--Output
12--16
16--19
20--22
24--25
26--26.5
Input--Output
1--3
2--5
3--9
4--17
5--33
Click here to see answer by stanbon(75887)

Question 1046870: Help on this input/output table please..
'Show & express the relationship using variables'
Input--Output
0-0
1-16
2-64
3-144
4-256
Click here to see answer by KMST(5328)

Question 1046894: Please help with this input output table
I need to know the equation
Input--Output
1--3
2--5
3--9
4--17
5--33
Click here to see answer by ewatrrr(24785)

Question 1047005: Identify the sequence as either arithmetic or geometric.
List the next two terms of the sequence.
9,2,-5,-12,?,?,?
Click here to see answer by Boreal(15235)

Question 1047005: Identify the sequence as either arithmetic or geometric.
List the next two terms of the sequence.
9,2,-5,-12,?,?,?
Click here to see answer by Timnewman(323)

Question 1047046: figure out the sequence of (1,2/3,3/5,4/7,5/9)
Click here to see answer by MathLover1(20850)

Question 1047085: write the summation notation for the following series. -7,3,13,23... and n=24
Click here to see answer by josgarithmetic(39617)

Question 1047092: hi I am learning pre-calculus 11 and am stuck on this question thank you!
Q. Determine the sum, Sn, for each arithmetic sequence described.
a) T1=7, Tn=79, n=8
they do not tell me what D is, so I am confused.. :)

Click here to see answer by Theo(13342)

Question 1047087: What is the explicit formula for the nth term of the series:
-6, -3, -2, -3/2, -6/5
Click here to see answer by stanbon(75887)

Question 1047121: 1,5,10,16,23,31 what is the next number in the sequence
Click here to see answer by Alan3354(69443)

Question 1047168: IF X=5, then 5x+2x =
Click here to see answer by MathLover1(20850)

Question 1047239: if the absolute value of difference bettween the 12th term and 9th term of an arithmetic progression is 27 and the square of the first term of the arithmetic progression is 9 is 27 , the 5th term of the arithmetic progression can not be
Click here to see answer by ikleyn(52787)

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