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

Tutors Answer Your Questions about Sequences-and-series (FREE)

Question 1162177: 4,16,68,292

Click here to see answer by ikleyn(52787)

Question 1162188: In an arithmetic progression, the sum of the first ten terms is 50 and the 5th term is three times the second term. Find the A. First term. B. Common difference. C. The sum of the first 100 terms

Click here to see answer by MathLover1(20850)

Question 1162263: Find the first 19 terms of the sequence an = 5n+2
Click here to see answer by ikleyn(52787)

Question 1162270: An exponential sequence is such that the third term minus the first term is 48. The fourth term minus the second term is 144. Find the common ratio, the first term, the sixth term
Click here to see answer by greenestamps(13200)

Question 1162437: My co-worker got this exercise from somewhere regarding number sequences, and we can't figure it out.
6, 78, 85, 8, 17, 24, 10, 34, ??
We can't see a pattern and it feels like we've covered everything out there.
Click here to see answer by greenestamps(13200)

Question 1162488: For an arithmetic progression, a1, a2, a3,..... aN, if a4/a7=2/3, find a6/a8.
Click here to see answer by greenestamps(13200)

Question 1162608: show tha the sum of n terms of the progression;
logx, logx^2, logx^3, logx^4, ... Is

n[n+1/2] logx
Click here to see answer by ikleyn(52787)

Question 1162725: The first and last term if an AP are -0.5 and 140.5, respectively.
(Q1) If the number of terms in the sequence is 48, find its common difference.
(Q2) the first term of an Arithmetic progression is -8. The ratio of the 7th term to the 9th term is 5 : 8, calculate the common difference of the progression
(Q3) show that each of the following sequence is an AP; 3n+4 14-4n and 4n-2
Click here to see answer by ikleyn(52787)

Question 1162806: find 139th term of the arithmetic sequence whose first term is -28 and the common difference is 1/3

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Question 1162673: If the sum of n terms of two arithmetic progressions is in the ratio (3n+8): (7n+15) find the ratio of their 12th term.
Click here to see answer by solver91311(24713)

Question 1162673: If the sum of n terms of two arithmetic progressions is in the ratio (3n+8): (7n+15) find the ratio of their 12th term.
Click here to see answer by greenestamps(13200)

Question 1162673: If the sum of n terms of two arithmetic progressions is in the ratio (3n+8): (7n+15) find the ratio of their 12th term.
Click here to see answer by ikleyn(52787)

Question 1162852: What is the general term of 3, 6, 11, 18

I think the common difference is 3+(n-2)

Click here to see answer by math_helper(2461)

Question 1162896: A plant grows 1.67 cm in its first week. Each week it grows by 2% more
than it did the week before. By how much does it grow in twenty weeks,
including the first week?

Click here to see answer by ikleyn(52787)

Question 1162895: An oil company bores a hole 80m deep. Estimate the cost of boring if the
cost is £30 for drilling the first meter with an Increase in cost of £2 per
meter for each Succeeding meter.
Click here to see answer by ikleyn(52787)

Question 1162919: the sum of the first four terms of a linear sequence(A.P)is 26 and that of
the next four terms is 74. Find the value of:
(¡) the first term;
(¡¡) the common difference.
Click here to see answer by Edwin McCravy(20056)

Question 1162917: find the sum to infinity of the series:
1+1/3+1/9+1/27/...
Click here to see answer by math_helper(2461)

Question 1162916: If Tn is the nth term of an exponential sequence, show that T1Tn=T2Tn-1
Click here to see answer by ikleyn(52787)

Question 1162979: Please help me find the sum of the following series:
t1 = -4
tn = 66
n = 15
Click here to see answer by ikleyn(52787)

Question 1162982: What position (n) in the sequence is the following?
tn = 680
t1 = 104
d = 16
Click here to see answer by ikleyn(52787)

Question 1162999: What is the common difference? An arithmetic series has 9 terms with a sum of -135. It has the first term of 9.
Click here to see answer by ikleyn(52787)

Question 1162999: What is the common difference? An arithmetic series has 9 terms with a sum of -135. It has the first term of 9.
Click here to see answer by MathTherapy(10552)

Question 1162999: What is the common difference? An arithmetic series has 9 terms with a sum of -135. It has the first term of 9.
Click here to see answer by greenestamps(13200)

Question 1162998: An arithmetic series has a sum of -823.5 with 27 terms. The first term is 5. Determine t27
Click here to see answer by ikleyn(52787)

Question 1162998: An arithmetic series has a sum of -823.5 with 27 terms. The first term is 5. Determine t27
Click here to see answer by greenestamps(13200)

Question 1163016: A plant grows 1.67 cm in its first week. Each week it grows by 2% more
than it did the week before. By how much does it grow in twenty weeks,
including the first week?
Click here to see answer by ikleyn(52787)

Question 1163020: The population p of a small town in t years from now is predicted to be p(t)=35000 + 10000/(t+2)^3. In your own method estimate the population of the town in the long run.

Click here to see answer by greenestamps(13200)

Question 1163035: The sum to infinity of a GP is twice the sum of the first two terms.
Find possible values of the common ratio.
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Question 1163034: A drilling machine is to have 8 speeds ranging from 100 rev/min to 1000
rev/min. If the speeds form a geometric progression determine their
values, each correct to the nearest whole number and explain your results.
Click here to see answer by greenestamps(13200)

Question 1163040: If the series {ak} satisfies that a1 = 1, and a2 = 2, and ak - 4a(k-1) + 3a(k-2) = 0 (k >= 0), then ak = (1 + p)/q. Find p and q for all values of k >= 1.
Click here to see answer by Edwin McCravy(20056)

Question 1163117: 1,8,27,64,125,?
Click here to see answer by josgarithmetic(39617)

Question 1163345: The nth term of a sequence is Tn=2+(n-2). Evaluate T3-T5
Click here to see answer by ikleyn(52787)

Question 1163501: how do i figure out what the next number is?
1,1,2,4,5,25?
Thank you
Click here to see answer by Edwin McCravy(20056)

Question 1163532: Please help me, solve this question. Find the next two numbers in the sequence. 69,101,121,...,....
Click here to see answer by ikleyn(52787)

Question 1163532: Please help me, solve this question. Find the next two numbers in the sequence. 69,101,121,...,....
Click here to see answer by Edwin McCravy(20056)

Question 1163647: Do you know how to solve that system? If not
post again asking how. The solutions are
A = 1/6, B = 0, C = 11/6, D = -1
Click here to see answer by ikleyn(52787)

Question 1163799: 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."
How do I approach this problem? I went through the questions that are already answered on this site as well as its Algebra II text book. I am still at a loss.
Thanks
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