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

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Question 918936: 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 MathTherapy(10552)

Question 918940: This year the number of students in a new school is 600. For the next 10 years the school will be taking 5 more students every year. How many students would have been taken in this school in 10 years?
Click here to see answer by josmiceli(19441)

Question 918867: first 3 terms of an infinite geometric sequence 16,8,4. Q1.Determine the nth term of the sequence.
Click here to see answer by MathLover1(20850)

Question 919054: Does the sequence a_n=1+(-1)^n converge?
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Question 919066: find 10th term in sequence whos fst 3 terms are 3,3,6 & each term aftr scnd term is sum of 2terms preceding it
Click here to see answer by rothauserc(4718)

Question 919071: 1 + 2 +4 + 5 +6 +8 ....59 , the sum of series is ? Its answer is 2000
Click here to see answer by KMST(5328)

Question 919492: Use Gauss approach to find the sum. (do not use formulas)

1+3+5+7+...+997

Click here to see answer by richwmiller(17219)

Question 919633: A theater has 32 rows of seats. If there are 26 seats in the 1st row, 30 in the 2nd, 34 in the 3rd and so on, how many seats are there in all?

Click here to see answer by mananth(16946)

Question 919714: Find the first three terms of f(n + 1) = f(n) + 8, if f(1) = 27.

Click here to see answer by ewatrrr(24785)

Question 919830: Which represents the nth term of the sequence 31,35,41,46,51?

Click here to see answer by Edwin McCravy(20056)

Question 919825: what are the next three numbers in this number series;
.1, .2, .3, .6, 1.1, 2.0, _, _, _ ?
Click here to see answer by Edwin McCravy(20056)

Question 917875: I would be thankful if someone kindly help me with this problem:
In an AP 3,7,11,... find the value of n for which the sum of the first 2n terms will exceed the sum of first n terms by 155.
I tried solving it as follows:
S2n = Sn + 155
2n/2 {2(3) + (n-1)(4)} = n/2 {2(3) + (n-1)(4)} + 155
Proceeding further I finally got:
2n^2 + n -155 = 0
This equation does not give the value of n as whole number.
Click here to see answer by Edwin McCravy(20056)

Question 919902: how many of the numbers between 1000 and 3000 begin or end with 2?
Click here to see answer by Edwin McCravy(20056)

Question 919991: the sum of two angles is 205. One angle is 26 less then twice the other. Find the angles.
Click here to see answer by ewatrrr(24785)

Question 920076: the recursive rule for a sequence is f(n) = f(n-1)/2 +5. The first term is 4. What is the third term?
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Question 920249: What is the common difference in these terms(1/4, 3/4, 5/4, 7/4)???
Click here to see answer by richwmiller(17219)

Question 920180: patterns 2,6,4,12,10,30,28,__,__,__
Click here to see answer by MathLover1(20850)

Question 916654: 1-the rth term in a sequence is 2+3r. Find the first three terms of the sequence.

Click here to see answer by mathsnight(4)

Question 920449: Given the formula A = 5b + 2c � d and A = 250, c = 50, and d = 20, what is the value of b?
Click here to see answer by Fombitz(32388)

Question 920464: 25, 44, 53, 62.....: what is the 12th term

Click here to see answer by ewatrrr(24785)

Question 920470: 25, 44, 53, 62 what is the 5th term
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Question 920521: What is the 3rd term of the sequence?
a1 = 4 and an = 3(an � 1)
a3 = _________
Click here to see answer by sofiyac(983)

Question 920521: What is the 3rd term of the sequence?
a1 = 4 and an = 3(an � 1)
a3 = _________
Click here to see answer by MathTherapy(10552)

Question 920521: What is the 3rd term of the sequence?
a1 = 4 and an = 3(an � 1)
a3 = _________
Click here to see answer by richard1234(7193)

Question 920794: if T (N) = 7 - N, what is the second term?

Click here to see answer by Fombitz(32388)

Question 920930: What is the rule and next term for the sequence -4 -3 -2 -1....?
Click here to see answer by ewatrrr(24785)

Question 921160:
Click here to see answer by srinivas.g(540)

Question 921027: 12,36,108,_,_ what the equation for this sequence
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Question 921258: How do we find the common ratio of a gp in which only the first n last terms r given
Click here to see answer by stanbon(75887)

Question 921266: Write these series using summation notation.
The sum of all even numbers from 20 to 60

The sum of all numbers that are the squares of integers that are less than 100.
Explain, like everything. None of this makes sense. Please O_o
Click here to see answer by Theo(13342)

Question 921514: Find the formula for the ninth term of sequence 34,36,18,10,2
First difference is 2,-18,-8,-8
So it's not linear
Second difference is -20,10,0
So it's not quadratic
Now I'm lost ?
Click here to see answer by josgarithmetic(39618)

Question 921969: I need some help understanding modula.
I put -101 mod 3 into a mod calculator and the answer comes up as 3.
Shouldn't it be 2?
-101 / 3 = 33 with 2 remaining.
Or does it change somehow with a negative?
Click here to see answer by rothauserc(4718)

Question 922008: sum of 49,44,39.....17terms

Click here to see answer by Fombitz(32388)

Question 922010: The Question:
"The nth term of a series is . Write down the (n+1)th term.
a) prove that the series is an arithmetic progression.
b) find, algebraically, the value for n for which the sum to n terms is 200"

-I have written the (n+1)th term
-I have also done part a) of the question by subtracting the nth term from the (n+1)th term to find that the common difference between the terms is 1.
-I also know that the formula for an arithmetic progression is
please help with part b) of the question
Click here to see answer by stanbon(75887)

Question 922031: Okay, so I'm having issues on how to find the nth term.. I know how to solve for the sum, which is what it wants me to do, but most of them dont give you the nth term.
Please explain what you did in each step? THANKS!!!!!
Calculate the sums of these series.
1.)
2.) this one scared me. I dont even think i know how to solve for the sum of this

Click here to see answer by josgarithmetic(39618)

Question 922288: A sequence of numbers is said to form a harmonic progression provided their reciprocals form an arithmetic progression. Insert three harmonic means between - 1/2 and 1/14.
Click here to see answer by KMST(5328)

Question 922624: What is the explicit formula of 5, 11, 23, 47?
Click here to see answer by josgarithmetic(39618)

Question 922690: In a geometric progression, the common ratio is -2 and the 8th term is -640. What is the first term?
Click here to see answer by srinivas.g(540)

Question 922689: In an arithmetic sequence the first term is -12 and the 15th term is 135. Find the common difference d.
Click here to see answer by srinivas.g(540)

Question 922706: Find the value of k so that 2k + 2, 5k - 11, and 7k - 13 will form an arithmetic progression.
Click here to see answer by srinivas.g(540)

Question 922706: Find the value of k so that 2k + 2, 5k - 11, and 7k - 13 will form an arithmetic progression.
Click here to see answer by MathTherapy(10552)

Question 922768: A = 5b + 2c � d and A = 250, c = 50, and d = 20, what is the value of b?
Click here to see answer by Fombitz(32388)

Question 922779: 30 + 12 (29-25)3 - 16 � 4
Divide: -560 � -40
Click here to see answer by Edwin McCravy(20056)

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