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

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Question 1189826: The first term of a G.P is x and 3rd term is y. Find an expression
for the common ratio in terms of x and y. the 1st and 3rd term of
a G.P are 8 and 18 respectively and the common ratio is positive,
find the common ratio.
Click here to see answer by ikleyn(52787)

Question 1189874: 71,53,11,81,33,77,39,47,54,77,76,....
Find next 3 numbers in the sequence but condition is that all numbers in sequence should be less than 100.

Click here to see answer by Edwin McCravy(20056)

Question 1189967: 16 , 6 , 68 , 88 , ? , 98
Click here to see answer by ikleyn(52787)

Question 1190141: A truck radiator holds 5 gal and is filled with water. A gallon of water is removed from the radiator and replaced with a gallon of antifreeze; then a gallon of the mixture is removed from the radiator and again replaced by a gallon of antifreeze. This process is repeated indefinitely. How much water remains in the tank after this process is repeated 3 times? 5 times? n times?
Click here to see answer by math_tutor2020(3817)

Question 1190152: Musical Frequencies
The frequencies of musical notes
(measured in cycles per second) form a geometric sequence.
Middle C has a frequency of 256, and the C that is an octave
higher has a frequency of 512. Find the frequency of C two
octaves below middle C.
Click here to see answer by math_tutor2020(3817)

Question 1190153: Bouncing Ball A ball is dropped from a height of 9 ft. The
elasticity of the ball is such that it always bounces up one-
third the distance it has fallen.
(a) Find the total distance the ball has traveled at the instant
it hits the ground the fifth time.
(b) Find a formula for the total distance the ball has traveled
at the instant it hits the ground the nth time.
Click here to see answer by Boreal(15235)

Question 1190117: A construction company purchases a bull-
dozer for $160,000. Each year the value of the bulldozer
depreciates by 20% of its value in the preceding year. Let V,
be the value of the bulldozer in the nth year. (Let n = 1 be
the year the bulldozer is purchased.)
Click here to see answer by Boreal(15235)

Question 1190184: What is the missing term in the series 1,6,15,28,40, ?

Click here to see answer by greenestamps(13200)

Question 1190184: What is the missing term in the series 1,6,15,28,40, ?

Click here to see answer by math_tutor2020(3817)

Question 1190223: a besieged fortress is held by 5700 men who have provisions for 66 days. of the garrison loses 20 men each day, for how many days will be provisions last?
Click here to see answer by ikleyn(52787)

Question 1190295: please help solve this: the nth term of a sequence is given by n²-4n-21.find the nth term which is equal to 24

Click here to see answer by MathLover1(20850)

Question 1190304: Please help me solve this math problem:If the sum of 1+2x+4x²+8x³+... 1¼. Find x
Click here to see answer by ikleyn(52787)

Question 1190304: Please help me solve this math problem:If the sum of 1+2x+4x²+8x³+... 1¼. Find x
Click here to see answer by math_tutor2020(3817)

Question 1190304: Please help me solve this math problem:If the sum of 1+2x+4x²+8x³+... 1¼. Find x
Click here to see answer by greenestamps(13200)

Question 1190303: Please help me solve this math problem:If the 10th term of a G.P is given 2^10 and the 20th term is given as 2^19.Find the first term, common ratio and the sum of the nth term
Click here to see answer by MathLover1(20850)

Question 1190378: Tn=3r+^n-1>0,15 the n^th term of a geometric sequence if the 3^red term 48,determine r

Click here to see answer by ikleyn(52787)

Question 1190377: Tn=3+^n-1>0,15 the n^th term of a geometric sequence if the 3^red term 48,determine r

Click here to see answer by ikleyn(52787)

Question 1190438: A quadratic pattern has a second term equal to 1 a third term equal to -6 and a fifth term equal to -14
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 greenestamps(13200)

Question 1190568: Please help solve this:16(x-1/x-8)²+8(x-1/x-8)+1=0
Click here to see answer by Alan3354(69443)

Question 1190567: Please help: the sum of the first two terms of a G.P is x.The sum of the last two is 1 if there are n term in all, calculate the common ratio
Click here to see answer by math_tutor2020(3817)

Question 1190566: 1) Profit per tree grown and sold depends upon the height of tree at the time of sale. Taking h as tree height in metres, profit of tree in thousands Tanzanian shillings is approximated as: P(h) = (10 + 2h) ^ (1/2) - 0.1h (1) What tree height provides maximum profit per tree? (2) What is the maximum profit per tree?
Click here to see answer by Theo(13342)

Question 1190617:
Consider the arithmetic series 3+7+11+15+19, answer the questions below
a (i) T1 and S1
(ii) Express T2 in terms of S2 and S1
(iii) T4 and S4
(iv) Express T3 in terms of S4 and S3
Use the pattern you observed in previous questions to express T100 in terms of S100 and S99

Click here to see answer by ikleyn(52787)

Question 1190688: How do i evaluate geometric series ?
Click here to see answer by ikleyn(52787)

Question 1190700: Sn = 8 + 10 + 12 + 14

1) Express T2 in terms of s1 and s2
2) express T3 in terms of S3 and S2
3)Express T4 in terms of S3 and S4

Click here to see answer by ikleyn(52787)

Question 1190712: in an arithmetic sequence, the first term is -5 and the common diffference is -5/6. What is the 6th term? the nth term?
Click here to see answer by ikleyn(52787)

Question 1190762: Number sequence: 23 27 24 32 23 ?
Click here to see answer by greenestamps(13200)

Question 1190762: Number sequence: 23 27 24 32 23 ?
Click here to see answer by Alan3354(69443)

Question 1190794: Find the sum of all-natural numbers from 100 to 300:
i) Which are exactly divisible by 4.
ii) Excluding those which are divisible by 4.
Click here to see answer by math_helper(2461)

Question 1190791: Split 69 into three parts such that they are in A. P. and the product of the two smaller parts is 483
Click here to see answer by math_helper(2461)

Question 1190791: Split 69 into three parts such that they are in A. P. and the product of the two smaller parts is 483
Click here to see answer by ankor@dixie-net.com(22740)

Question 1190791: Split 69 into three parts such that they are in A. P. and the product of the two smaller parts is 483
Click here to see answer by greenestamps(13200)

Question 1190793: Find three numbers in GP such that their sum is 39 and their product is 729
Click here to see answer by Alan3354(69443)

Question 1190793: Find three numbers in GP such that their sum is 39 and their product is 729
Click here to see answer by greenestamps(13200)

Question 1190792: Find the sum of positive integers between 100 and 999 inclusive which are odd.
Click here to see answer by ikleyn(52787)

Question 1190781: 3 7 11 15 19 23 express T1 in terms of S1, express T2 in terms of S1 and S1
Click here to see answer by ikleyn(52787)

Question 1190815: 1/t+3/t+5/t.....+t-1/t determine the number of terms in the series in terms of t

Click here to see answer by greenestamps(13200)

Question 1190888: 2,x,y,-250
Click here to see answer by Alan3354(69443)

Question 1190995: Please help me find the following term of sequence 4.75,10.5,16, 21, _ and the nth term. Thank you very much.
Click here to see answer by greenestamps(13200)

Question 1191149: The sum of the first two terms of an exponential sequence is 135 and the sum of the third and the fourth terms is 60.given that the common ratio is positive.calculate:the limit of the first n terms as n becomes larger and the least number of terms for which the 7um exceeds 240.
Click here to see answer by greenestamps(13200)

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