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 869501: If 8,x,y,z,20.find x,y,z and show the working
Click here to see answer by Fombitz(32388)

Question 869535: 63,61,53,21
The answers are:
-128
-11
-32
-107
I am not sure which
Click here to see answer by Fombitz(32388)

Question 869548: Dear people,
I cannot seem to solve this sequence/problem:
60 65 63 68 75 74
I would be very grateful if someone could show me how.
And If I am correct the answers to this problem: 23 28 30 29 is 33?
Click here to see answer by richard1234(7193)

Question 869683: Prove that the sum of AP is sn equals(2a+(n-1)d)
Click here to see answer by stanbon(75887)

Question 869790: Q. What is the next number of the following sequence
1, 2, 5, 10, 25, 50, ___

Click here to see answer by ramkikk66(644)

Question 869790: Q. What is the next number of the following sequence
1, 2, 5, 10, 25, 50, ___

Click here to see answer by richwmiller(17219)

Question 869789: Solve it:
a=13
b=29
c=48
d=60
e=?
The right answer is 65. Tell us the logic
Click here to see answer by ramkikk66(644)

Question 869837: What are the first four terms in the multiplication pattern given by the formula?
4 � 3n

A.
4, 12, 36, 108

B.
7, 21, 63, 189

C.
12, 36, 108, 324

D.
12, 24, 36, 48
Click here to see answer by Fombitz(32388)

Question 869934: Joe drove 355 miles using 17 gallons of gas. At this rate, how many gallons of gas would he need to drive 284 miles?
Click here to see answer by Alan3354(69443)

Question 870009: The 5th term of an arithmetic progression is three times the first term.find the sum of the first eight terms of the progression given that a quarter of the fifth term is 9
Click here to see answer by mananth(16946)

Question 870008: The sum of the first ten terms of a linear sequence is -60 and the sum of the first fifteen terms of the sequence is-165.find the 18th term of the sequence
Click here to see answer by mananth(16946)

Question 870010: The sum of the 4th and 6th term of an arithmetical progression is 42.the sum of the 3rd and 9th terms of the progression is 52.find the first term,the common difference and the sum of the first ten terms of the progression.
Click here to see answer by mananth(16946)

Question 870152: Please help me find the equation for this and how to get the answer to what it's looking for.
Five years ago the population of a city was 49,000. Each year they permit an increase of 580 in the population. What will the maximum population be 5 years from now?
Click here to see answer by checkley79(3341)

Question 870144: I have been given the following sequence of numbers: 100, 365, 24, 60.
I have been asked to give the next number in the sequence. I have tried to find the pattern, looked at percentages, square roots, anything I can think of and have yet to find the key.
If you just want to give me a hint instead of the answer, I will continue to try and figure it out myself.
Thanks.
Click here to see answer by checkley79(3341)

Question 870247: Consider the sequence 16, -8, 4, -2, 1,...
a.) Describe the pattern formed in the sequence.
b.) Find the next three terms.
Click here to see answer by josgarithmetic(39618)

Question 870050: Find an A.P. if t4 = 12 & d = -10, then find its general term?
Click here to see answer by richwmiller(17219)

Question 870250: What is the fourth term in given sequence?
3,1.5,1,?
Click here to see answer by richwmiller(17219)

Question 870376: Find the tenth term of the arihmetic sequence in which a1=6 and d=5
some work i have done: an=6+(n-1)5
an= 6+5n-5
Click here to see answer by richard1234(7193)

Question 870504: Write an explicit formula for 1/2, 1/4, 1/6, 1/8, 1/10...
I have tried a subscript n= 1/2n

Click here to see answer by jim_thompson5910(35256)

Question 870528: Evaluate each series to the given term.
2+4+6+8+...10th term
Click here to see answer by mananth(16946)

Question 870500: Suppose that the eighth term of an arithmetic sequence is 59, and also suppose that the twenty first
term of the same arithmetic sequence is 150. Find an explicit formula for the general term of this
arithmetic sequence.
Click here to see answer by mananth(16946)

Question 870537: Write the first six terms of each of the sequences whose nth term is
(-1)^n(n)
(100)(-1/2)^n
Click here to see answer by KMST(5328)

Question 870810: Find the 15th term
17, 23, 29, 35..

Click here to see answer by ewatrrr(24785)

Question 870726: insert two geometric means between 3 and 48
Click here to see answer by richwmiller(17219)

Question 870848: 1. If a person eat 100 bananas in 5 days. He eats 6 more bananas than the previous day. How many bananas does he eat on the 5th day?
Click here to see answer by richwmiller(17219)

Question 871122: if 4x+5y = 216 & x+y = 48, then what is the value of x & y ?

Click here to see answer by ewatrrr(24785)

Question 871373: what is rule for the nth term for -2+4-8+16-32.
1,2,3,4,5 is i
Example:
5+11+17+23+29
i6-1
(1*6)-1=5
(2*6)-1=11
(3*6)-1=17
Click here to see answer by Edwin McCravy(20056)

Question 871381: A recursive formula for the following series: 1, 3/2, 5/6, 7/24, 9/120
Click here to see answer by KMST(5328)

Question 871381: A recursive formula for the following series: 1, 3/2, 5/6, 7/24, 9/120
Click here to see answer by richwmiller(17219)

Question 871510:
Click here to see answer by lenny460(1073)

Question 871901: given the explicit formula for a geometric sequence is an=3(-2)n-1. What is the fifth term of the sequence? I came up with a5= 1296, but am not sure.

Click here to see answer by mananth(16946)

Question 871900: How many multiples of 3 less than 100 can be formed from the digits 1 4 5 7 8
(hint: the sum of the digits of any multiple of 3 is also a multiple of 3.)
Click here to see answer by richwmiller(17219)

Question 872382: I just had a simple question.
This is really going to sound pathetic and its really like grade 1 maths but for the life of me I cannot figure out the proof of this formula.Here is the proof:
Geometric Progression = a + ar + ar^2 + ar^3 + ... + ar^n-1 (1)
multiply formula (1) by r: r.GP = ar + ar^2 + ar^3 + ... + ar^n-1 + ar^n (2)
subtracting formula (2) from (1)gives: GP- r.GP = a -ar^n
factoring on both sides gives: GP(1-r)=a(1-r^n)
dividing by (1-r): GP= a(1 -r^n)/ (1-r)
My problem in the proof is not the logic behind it its the mechanics of the maths in line 2 of the proof where formula 1 gets multiplied through by r, for the life of me I dont understand why by multiplying through by "r" it leaves the term "ar^n-1". I though by multiplying the term ar^n-1 in the first formula it leaves ar^n due to the laws of exponents thus I do not see where the original term comes from in the second line. Its probably one of the most fundamental laws of algebra and I feel really bad not being able to get it, I just would really like some help on it please.
P.S. I got the proof from this url http://www.mathcentre.ac.uk/resources /workbooks/mathcentre/APGP.pdf page 9 at the bottom.
Click here to see answer by stanbon(75887)

Question 872386: A geometric sequence has a1 = 16 and r = \sqrt{2}2, what is the sum of the first 21 terms?
Click here to see answer by richwmiller(17219)

Question 872532: A)What are the terms missing from the geometric sequence below?
___, -11 , 22, ___, 88 , -176
B) Write a recursive equation for x n + 1.. if possible. Thanks.

Click here to see answer by rothauserc(4718)

Question 872512: List the first 10 terms of each of these sequences ,
a)the sequence that begins with 2 and in which each successive term is more than the preceding term.
b)the sequence that lists each positive integer three times,in increasing order .
c)the sequence that lists the odd positive integers in increasing order,listing each odd integer twice.
d)the sequence whose n th term is n!-2n.
Click here to see answer by KMST(5328)

Question 872714: 6 , 13 , 25 , 52 , 101 , ?
Click here to see answer by Edwin McCravy(20056)

Question 872663: Prove that there exist some n
such that
(x^n)^2=x^n for all n>= 1.
r is idemotent ring where x^2= x
I have more this one is just to check who is qualified to help me
Click here to see answer by rothauserc(4718)

Question 872853: Please help me solve this induction question using a direct proof:
Prove by induction that n! < n^n, for positive integers n >= 2
Click here to see answer by jim_thompson5910(35256)

Question 872908: Two terms of an arithmetic sequence are a5=11 and a32=65. Find a rule for the nth term.
Click here to see answer by stanbon(75887)

Question 872909: John has 100 pages to read over 5 days. He wants to increase the number of pages he reads by 5 pages each day.
a. How many pages should he read the first day?
b. John learns that he has 200 pages to read. If he reads twice as many pages the first day, then increases the number of pages he reads by 5 pages a day, will he read twice as many pages? Explain your reasoning.
Click here to see answer by ewatrrr(24785)

Question 872865: In a progression, the third term has a value of 7 and the tenth term has a value of 17.5. Determine the values of the first term; the common difference if it is an AP and the common ratio if it is a GP.
Also, find the sum of the first two terms in each case.
Please help me, I've been struggling on this question for hours!
Thank you so much!
Click here to see answer by rothauserc(4718)

Question 872946: Arrange the list of numbers in increasing order 2/5,4/9,3/7

Click here to see answer by ewatrrr(24785)

Question 867268: 3, -6, 12, 4, 20, ?
Click here to see answer by richwmiller(17219)

Question 873019: Use the formula to evaluate the series 3-9+27-81+...-a8?
Click here to see answer by ewatrrr(24785)

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