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

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Question 1159031: find the sum of the infinite geometric series
http://prntscr.com/sg30qg
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Question 1159079: The 1st,2nd and 3rd terms of an arithmetic progression are 8-x,3x and 4x+1 respectively calculate the value of x
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Question 1159112: find the sum of the finite geometric sequence
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Question 1159111: find the sum of the finite geometric sequence
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Question 1159207: The legs of a right triangle are 12 centimetres and 16 centimeters. What is the length of the hypotenuse?
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Question 1159429: The sum of the original sequence is 1
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Question 1159435: What is this pattern
2, ?, ?, 23, ?, 37

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Question 1159435: What is this pattern
2, ?, ?, 23, ?, 37

Click here to see answer by greenestamps(13200)

Question 1159435: What is this pattern
2, ?, ?, 23, ?, 37

Click here to see answer by josgarithmetic(39617)

Question 1159522: I have a problem so I have 72-11=63 then 63-A=B B-45 45-9-36 then 36-C=D
What is ABC and D?
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Question 1159596: a^(1)=18,r=3,n=6
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Question 1159595: a^(1)=3,r=-2,n=5
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Question 1159602: A+B=10
C/D=4
A+C=3
B+D=9
Click here to see answer by Alan3354(69443)

Question 1159602: A+B=10
C/D=4
A+C=3
B+D=9
Click here to see answer by josgarithmetic(39617)

Question 1159602: A+B=10
C/D=4
A+C=3
B+D=9
Click here to see answer by greenestamps(13200)

Question 1159681: Find the 83rd term of the arithmetic sequence -23, -26, -29, ...−23,−26,−29,
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Question 1159692: a^(1)=-78,125, r=1/5, n=9
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Question 1159691: a^(1)=-20, r=-2, n=9
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Question 1159693: What is the next value in these sequences?
(A) 85, 13, 26, 8, 16, ?
(B) 1, 5, 14, 30, 55, ?
Many thanks!!
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Question 1159788: The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the 20th term?
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Question 1159788: The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the 20th term?
Click here to see answer by MathTherapy(10552)

Question 1159787: The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the common difference?
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Question 1159786: The fifth term of an arithmetic progression is three times the second term,and the third term is 10.find the first term?
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Question 1159839: There are 40 pupils in a class. Each girl is given 5 books and each boy is given 4 books. The girls have 65 more books than the boys. How many more girls than boys are there in the class?

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Question 1159888: What is the next number in the series 9, 11, 22, 15, 17, 34, 25, 27, 54, 43, 45, 90?
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Question 1159888: What is the next number in the series 9, 11, 22, 15, 17, 34, 25, 27, 54, 43, 45, 90?
Click here to see answer by greenestamps(13200)

Question 1159891: 1, 16, 61, 76, 67, 82, 28 What is the next number?
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Question 1159891: 1, 16, 61, 76, 67, 82, 28 What is the next number?
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Question 1159890: 4/3, -2/3, -1/3, 1/6, 1/12, -1/24 What is the next number?
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Question 1159890: 4/3, -2/3, -1/3, 1/6, 1/12, -1/24 What is the next number?
Click here to see answer by greenestamps(13200)

Question 1159889: What is the next number in the series 4/3, -2/3, -1/3, 1/6, 1/12, -1/24?
Click here to see answer by ikleyn(52787)

Question 1159907: The nth term t(n),of a sequence is given by t(n)=p+nq,where p and q are constants.find the sum of the first 6 term in terms of p and q
Click here to see answer by greenestamps(13200)

Question 1159906: The nth term t(n),of a sequence is given by t(n)=p+nq,where p and q are constants.write down the 6th term of the sequence in term of p and q
Click here to see answer by greenestamps(13200)

Question 1160024: What is next number and why??
2,4,9,3,8,5,7,6,10,1
Thnx..

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Question 1160027: write an explicit formula for the sequence 7, 2, -3, -8, -13,... then find a_14
http://prntscr.com/sob4im
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Question 1160027: write an explicit formula for the sequence 7, 2, -3, -8, -13,... then find a_14
http://prntscr.com/sob4im
Click here to see answer by MathLover1(20850)

Question 1160027: write an explicit formula for the sequence 7, 2, -3, -8, -13,... then find a_14
http://prntscr.com/sob4im
Click here to see answer by josgarithmetic(39617)

Question 1160055: Three different interger that the sum is 1 and product is 36
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Question 1160078: 1. Find the 25th term of the arithmetic sequence
‒7, ‒4, ‒1, 2, ...

2. In an arithmetic sequence, if a4 = 18 and a10 = 30, determine a1, d, and an.
Then write the first four terms of the sequence.

3. In a geometric sequence, if a3 = ‒5 and a6 = 40, determine a1, r, and an.
Then write the first three terms of the sequence.

Click here to see answer by MathLover1(20850)

Question 1160066: The nth term t(n),of a sequence is giving by t(n)=p+nq,where p and q are constants.find the sum of the first 6 terms in terms of p and q.
Click here to see answer by Edwin McCravy(20056)

Question 1160065: The nth term t(n),of a sequence is giving by t(n)=p+nq,where p and q are constants.write down the 6th term of the sequence in term of p and q.
Click here to see answer by ikleyn(52787)

Question 1160063: A G.p is such that the third term is 9 times the first term, while the second term is one- twenty fourth of the fifth term. find it's Fourth term
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Question 1160228: Find S20 for the arithmetic series 24+16+8 + … .
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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