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 860832: How do I find the sum of the first 100 positive integers?
I tried doing with Sn=150 but that isn't correct
I got the 100 because it's the first 100 positive integers so I assumed the final integer was 100.
Click here to see answer by ewatrrr(24785)

Question 860737: if r=-3 and a5= 486 what is the first item in the sequence
Click here to see answer by richwmiller(17219)

Question 860749: pat designs a patio consisting of 16 row
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Question 860723: given a1=94 the common difference is -3, find n so that sn=805. (hint: you will use -b square root b squared -4ac divided by 2a to solve for n)
Click here to see answer by richwmiller(17219)

Question 860707: pat designed a patio consisting of 16 rows of congruent slate tiles. the number of tiles in the rows form an arithmetic sequence. the first row contains 15 tiles and the last row contains 30 tiles. how many tiles are used in the deck?
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Question 860896: 1764= n/2(12+174)
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Question 860598: The variance of first 50 even natural numbers is
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Question 861041: 1)
Given that for an AP seventh term=43 and second term=91,find the valves of a,d and n.(11).
2)
The first term of an AP is -18 and the last term is 115.If the sum of the progression is 970.Find the number of terms in the AP and the common difference.
Click here to see answer by richwmiller(17219)

Question 861158: Select the two numbers which should appear next in the series. 3 9 5 15 11 33 29
Click here to see answer by ben720(159)

Question 861192: Find the coefficient of the fourth term in ascending powers of x in the expansion of (1 -x+x raised to power 2) all raised to power 7
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Question 861188: Find the 6th term of geometric sequence with the given terms
A4=-12 a5=-4
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Question 861184: The first term of an AP is 7, the last term is 77 and the sum is 380. Find the common difference in the series.
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Question 861357: I need explanation and solution:
The product of four consecutive natural numbers is 255024. Find these numbers.

Click here to see answer by mananth(16946)

Question 861357: I need explanation and solution:
The product of four consecutive natural numbers is 255024. Find these numbers.

Click here to see answer by richwmiller(17219)

Question 861348: Given that for an AP seventh term=43 and second term=91,find the valves of a,d and n.
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Question 861420: A vacuum claims to pick up 80% of the dirt every time it is run over the carpet. Assuming this is true, what percent of the original amount is picked up after the seventh time the vacuum is run over the carpet?
Click here to see answer by richwmiller(17219)

Question 861660: y varies directly as x and inversely as the square of z. y=24 when x=12 and z=2. Find y when x=64 and z=4.
y=

thank you so much!
Click here to see answer by richwmiller(17219)

Question 861778: Find the sum of x and y when: x^2+y^2+136=4(5y-3x)
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Question 861717: 6-9-?-24-36
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Question 861957: what is the 6th 9th and 12th terms in a sequence?

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Question 862100: Consider the sequence 130, 143, 156, 169, ...

Write an explicit formula to represent the arithmetic sequence and use it to find the 13th term.

A. A(n) = 130 + (n-1)13; 286
B. A(n) = 130 + 13n; 299
C. A(n) = 130 + (n-1)13; 299
D. A(n) = 130 + 13n; 286
Click here to see answer by richwmiller(17219)

Question 860986: variance of first 50 natural even number
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Question 862211: What is the next number in this sequence 9 10 11 12 13 14 100
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Question 862285: Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence.
2, 4, 8, 16, �32, 64, �
Click here to see answer by josgarithmetic(39617)

Question 862288: Use the formula below to find the 25th term in the geometric sequence.
a[n]=(-3)2^n-1
Click here to see answer by ewatrrr(24785)

Question 862286: A geometric sequence has a term of a4= �54 and a common ratio of r = 3. What is the rule for the nth term?
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Question 862286: A geometric sequence has a term of a4= �54 and a common ratio of r = 3. What is the rule for the nth term?
Click here to see answer by Theo(13342)

Question 862408: Prove by mathematical induction
+ ...+

Click here to see answer by Edwin McCravy(20056)

Question 856871: If 1/(y+ax),1/(2y),1/(y+az) are in arithmetic progression.prove that k^2x,y, z are in geometric progression
Click here to see answer by Edwin McCravy(20056)

Question 862775: For each sequences
1.Continue the pattern for three more terms
2.Describe the rule or pattern of the sequence in words
3.Write a formula for the general term fir each sequence
(a) 2,4,6, , , , ,
(b)5,10,15, , , ,
(c)1,4,9, , , , ,
(d)10,20,30, , , , ,
e)2,5,10, , , , , ,
f)18,27, , , , , ,
g)2,9,28, , , , ,
h)4,7,10, , , , ,
Click here to see answer by checkley79(3341)

Question 862795: find a general term an for the sequence a1=5 D=-2
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Question 862809: . The ﬁrst term in a sequence is 400 . Every subsequent term is 20 less than half of the immediately
preceding term. What is the 4th term in the sequence?

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Question 862868: y varies directly as x and inversely as the square of z.
Y=24 when X=12 and z=2. Find y when x=64 and z=4
y=
Only question on my homework i can't figure out! Thank you!
Click here to see answer by Alan3354(69443)

Question 862875: Give the first four terms of the geometric sequence for which a1=7 and r=5
Click here to see answer by josgarithmetic(39617)

Question 862879: write a recursive rule for the sequence 1, 1/2, 1/2, 3/4, 3/2,...
Click here to see answer by Edwin McCravy(20056)

Question 862880: Find the first four terms of the sequence an= n(5n +3)

Click here to see answer by richwmiller(17219)

Question 862874: In a financial deal, you are promised $100 the first day and each day after that you will receive 45% of the previous day's amount. When one day's amount drops below $1, you stop getting paid from the day on. What day is the first day you would receive no payment and what is your total income?
Click here to see answer by richwmiller(17219)

Question 863255: Hi I have a problem with formula for series.
The 1st 5 numbers are: 5, 10, 17, 26, 37.
As you can see differences have differences themselves. I know the sequence would be quadratic because I worked it out: n^2+2n+2
Next part of the question is how many blocks is it needed for 21 patterns.
Formula for series with constant difference is there. But the difference is changing so I don't know what to do, or what to google.
Click here to see answer by rothauserc(4718)

Question 863226: Please help me solve this question: The first three terms of an arithmetic progression are -1049, -1046, -1043.
Which term of this progression will first be positive?
Click here to see answer by richwmiller(17219)

Question 863039: Please help me in answering this problem:
The unit measure for atmospheric pressure is KPa (Kilo-Pascals). At sea level the standard atmospheric pressure is 101.3 KPa. For every 1000 feet increase in altitude atmospheric pressure decreases by 1.8 KPa.
What is the atmospheric pressure at 50,000 feet?
I have tried to answer the question, my understanding to the question is what is the value of t 50,000 and the common difference d is 1000 but I didn't know if I should consider the first term (a)= 101.3 or 101.3 - 1.8 = 99.5 KPa
Thank you
Click here to see answer by richwmiller(17219)

Question 858581: If the position of the digit of a two digit number are interchanged ,the number obtained is smaller than the original number by 27. If the digits of the number are in the ratio 1:2,what is the original number?
Click here to see answer by richwmiller(17219)

Question 863286: if 5=2 and 9=0 and 13=1 then 17=?.
Click here to see answer by richard1234(7193)

Question 863632: an=(-1/3)^n
The first n is lower than the a but not sure how to type it. Thanks
Click here to see answer by Fombitz(32388)

Question 863643: write the ﬁrst four terms of each sequence
whose general term is given.
an=(-1/3)^n
Click here to see answer by stanbon(75887)

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