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 1074837: -5, 10, -15, 20 find the nth term rule
Click here to see answer by josgarithmetic(39618)

Question 1074837: -5, 10, -15, 20 find the nth term rule
Click here to see answer by MathTherapy(10552)

Question 1074866: i need the next number in sequence 2,8,6,56,18,?

Click here to see answer by ikleyn(52788)

Question 1074887: Given:

The following table represents the operation # on the set G = {a, b, c, d}
# a b c d
a a b c d
b b c d a
c c d a b
d d a b c
A. Explain why the set G is closed under the operation #.

B. Explain why a is the identity element for #.

C. Verify two cases of the commutative property.
Click here to see answer by Fombitz(32388)

Question 1074793: a man gets an employment of rs 6500 per month with an annual increment of rs 500. what will be his monthly salary after 15 years and what will be the total amount he earns in 15 years
Click here to see answer by Theo(13342)

Question 1074938: 7,9,-1,5, n what is n?
Click here to see answer by Edwin McCravy(20056)

Question 1074919: show that the following series converges absolutely for |x|<1 and compute the sum.
f(x)=1-x-x^2+x^3-x^4-x^5+x^6-x^7-x^8+...
The hint we were given was to write f(x) as the sum of 3 geometric series with a common ratio of x^3
Click here to see answer by KMST(5328)

Question 1075177: Sum of second and third is 6, third and fourth is -12. Find the common ratio
Click here to see answer by josgarithmetic(39618)

Question 1075167: Where does this sequence come from?
1, 8, 9, 16, 17, 24, 25, 32, 33, 40, 41, 48, 49, 56, 57, 64, 65, 72, 73, 80, 81, 88, 89, 96, 97, 104, 105, 112, 113, 120, 122, 125, 129, 134, 140, 147.
??
Click here to see answer by rothauserc(4718)

Question 1075196: Hello,
could I please have some help with this question,
Prove by mathematical induction that;
(1 � 2) + (3 � 4) + � � � + (2n − 1) � 2n = n(n + 1)(4n − 1)/3
for all n ∈ N.
Click here to see answer by KMST(5328)

Question 1075231: What is the first term of a sequence when the eighth term is twice the third term and the sum of the first eight terms is 39?
Click here to see answer by Boreal(15235)

Question 1075313: determine the value of m so that 2m+1, m, and 5-3m form an arithmetic progression
Click here to see answer by Boreal(15235)

Question 1075313: determine the value of m so that 2m+1, m, and 5-3m form an arithmetic progression
Click here to see answer by Theo(13342)

Question 1075525: An arithmetic sequence has its 5th term equal to 22 and its 15th term equal to 62. Find a recursive formula and a formula for the nth term. Label which is which.
a5 =22 and a15 =62 but I don't know how to go on from that point..
Thanks so much for the help:)
Click here to see answer by Boreal(15235)

Question 1075535: write the series -7,-4,-1,2,... using summation notation
Thank you:)
Click here to see answer by Lightning_Fast(78)

Question 1075574: 1,3,9,27,45
Click here to see answer by ikleyn(52788)

Question 1075550: Explain how to use patterns or sequences to determine the last digit of the number 7N, where N is the four-digit year of your birth.
Click here to see answer by ikleyn(52788)

Question 1075416: Find the first term and the common difference for the arithmetic sequence. Round approximations to the nearest hundredth.
S5=75, a5=33
Click here to see answer by Boreal(15235)

Question 1075432: I've been stuck on these problems, I've figured out parts of each question but need help with it!
When the SuperBall� was introduced in the 1960�s, kids across the United
States were amazed that these hard rubber balls could bounce to 90% of the
height from which they were dropped.
a. Is this problem an example of a geometric series or an
arithmetic series? Support your answer mathematically by applying the
concepts from this unit.

b. If a SuperBall� is dropped from a height of 2m, how far does it
travel by the time it hits the ground for the tenth time? (Hint: The ball
goes down to the first bounce, then up and down thereafter.)
To figure this problem out, one way I would solve this problem is to use
the formula An=2 (.90)^n-1 , then to get a11 we plug in the info we know,
to get 2(.9)^10 to get an answer of aout .70m

2. You borrowed $5,000 from your parents to purchase a used car.
You have agreed to make payments of $250 per month plus an additional 1%
interest on the unpaid balance of the loan.
a. Is this problem an example of a geometric series or an
arithmetic series? Support your answer mathematically by applying the
concepts from this unit.

b. Find the first year�s monthly payments that you will make and
the unpaid balance after each month.

c. Find the total amount of interest paid over the term
of the loan
Thanks!
Click here to see answer by Boreal(15235)

Question 1075584: Provide the first five terms of an arithmetic or geometric sequence that has a first term higher than 10 and a common difference or ratio that is positive but not 1.
1.� Explain how to determine the nth term formula.
2.� Find the 30th term, showing all work.
�
B.� Explain how to use patterns or sequences to determine the last digit of the number 7^N, where N is the four-digit year of your birth.

Click here to see answer by ikleyn(52788)

Question 1075814: Which three out of the following equals 30?
1 3 5 7 9 11 13 15
Click here to see answer by Alan3354(69443)

Question 1075863: If a+b=6, b+c=−3, and a+c=5, what is the value of a+b+c?
Click here to see answer by ikleyn(52788)

Question 1075947: the sum of the first and last terms of an arithmetic progression is 42.the sum of all the terms is 420.If the second term is 4,find the number of term,common difference,last term of the sequence
Click here to see answer by ikleyn(52788)

Question 1075914: What is the next number in this pattern 8, 10, 5, 6, 16, ?
Click here to see answer by ikleyn(52788)

Question 1075903: What is the next number in this pattern 314, 622, 212, 123, 664, ... ?
Click here to see answer by ikleyn(52788)

Question 1075903: What is the next number in this pattern 314, 622, 212, 123, 664, ... ?
Click here to see answer by vanvanpro(2)

Question 1075941: What sequence follows (5,12), (6,10), (15,4), ..........?
Click here to see answer by ikleyn(52788)

Question 1075976: find the sum of the following sequence: 3, 7, 11, 15,..., 79?
Click here to see answer by josgarithmetic(39618)

Question 1075976: find the sum of the following sequence: 3, 7, 11, 15,..., 79?
Click here to see answer by stanbon(75887)

Question 421300: What is the next two number of this sequence?
13 6 11 9 9 12 7 _ _
Click here to see answer by vanvanpro(2)

Question 1076020: Write the following series in summation notation please?
12+6+3+1.5+0.75
Click here to see answer by KMST(5328)

Question 1076021: what is the first five terms of the sequence a1=3, and an=2an-1
Click here to see answer by Fombitz(32388)

Question 1076171: R0: 3,6,9,12,15,18,21,...
R1: 1,4,7,10,13,16,19,...
R2: 2,5,8,11,14,17,20,...
a) Write down an expression for the value of the general term in each of the three prgressions. Show that the integer 1706836 lies in R1. I got R0:3n, R1:3n-2 and R2:3n-1. Then i did 3n-2=1706836 and showed that n=568946, so it lies in R1 and is the 568946th term in the series.
b) Use the Binomial Theorem to show that if x is a term in R1 or R2 then x^6 is in R1. This is the part i don't know how to work out.
Click here to see answer by KMST(5328)

Question 1076287: find the sum of ap 2+5+8+,...as far as the 18th terms
Click here to see answer by josgarithmetic(39618)

Question 1076234: Write the series using summation notation -3+17+117+...
Click here to see answer by Edwin McCravy(20056)

Question 1076392: The sum of ten numbers in an arithmetic progression (sequence) is 190. The sum of the fourth and eighth term exceeds the fifth term by 25. Find the first four terms of the sequence. Only an algebraic solution will be accepted.
Click here to see answer by josgarithmetic(39618)

Question 1076321: how do i find the geometric means of this sequence 7/2, _ , _ , _ ,56/81

Click here to see answer by Edwin McCravy(20056)

Question 1076576: Akim runs 1.75 miles on his first day of training for a road race. The next day, he increases his distance run by 0.25 miles. The day after that, he increases his distance run by another 0.25 miles, and so on.
What is the total number of miles Akim runs over the course of 18 days?
68.5 mi
69.75 mi
70.25 mi
72.5 mi
Click here to see answer by Boreal(15235)

Question 1076457: the numbers of seats in the first 12 row of a high school auditorium form an aritmetic sequence the first row has 9 seats the second row has 11 seats write a recursive formula to represent the sequence. write an expicit formula to represent the sequence. how many seats are in the 12th row
Click here to see answer by Herdaysoji(25)

Question 1076692: Help! Need to find the missing number in the sequence: 1, 4, 27, ___?___, 3125
Thank you!
Click here to see answer by math_helper(2461)

Question 1076734: How many GP are possible contaning 27,8 and 12 as three of their terms
1(1)
2(2)
3(4)
4(infintely many)
Click here to see answer by josgarithmetic(39618)

Question 1076783: In an a.p the sum of the squares of the five consecutive series is 20time the square of the middle term,and the product of the five terms equals to 80.What is the middle term.

Click here to see answer by ikleyn(52788)

Question 1076854: the sum of the squares of five consecutive a.p is 55,and their product is 120.what are the numbers.
Click here to see answer by ikleyn(52788)

Question 1076928: Two dice are thrown.given that the sum of the dice is 8,what is the probability that one 5 is cast?
Click here to see answer by alanc(27)

Question 1076920: What is the next number in this sequence
5 3 9 12 10 30 33 31 93
Click here to see answer by Boreal(15235)

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