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 360975: Sum of a number and 15 is 96. Find the number.
Click here to see answer by Fombitz(32388)

Question 361815: Find the sum of the rest 20 terms of the following series: 4 + 12 + 36 + 108...
Click here to see answer by robertb(5830)

Question 361865: a besiege fortress is held by 5700 men who have provision for 66 days. if the garrison losses 20 men each day, for how many days can the provision hold out?
Click here to see answer by robertb(5830)

Question 361872: How to determine whether the series converges or diverges?
1/16+1/49+1/100+1/169+...

Click here to see answer by robertb(5830)

Question 362359: Find two numbers (exactly) whose product is 54 and whose sum is 23.
Click here to see answer by Fombitz(32388)

Question 362992: How to determine whether the sequence converges or diverges?
7,23,55,109
Click here to see answer by Edwin McCravy(20056)

Question 363788: If a 50g sample of substance Z decays to 47g in 11 days, what is the half-life of substance Z? Give your answer to the nearest day.
Click here to see answer by amoresroy(361)

Question 363799: The people of Vancouver cannot keep a secret. Upon being told a secret, a person from Vancouver will spend the next hour telling 3 friends the secret. In turn, those 3 friends will spend the next hour each telling 3 more people. This process continues and no one will tel someone who already knows the secret. If you tell a person from Vancouver a secret, how many people, excluding you, will know the secret in 7 hours?
Click here to see answer by amoresroy(361)

Question 363860: A weather balloon rises 150 meters the first minute after it is released. Each minute, it rises 6% slower than the previous minute, How far does the balloon travel in 15 minutes? Give your answer to the nearest tenth.
Click here to see answer by amoresroy(361)

Question 363967: what are the two consecutive # whose sum is 21?
Click here to see answer by Alan3354(69443)

Question 363967: what are the two consecutive # whose sum is 21?
Click here to see answer by stanbon(75887)

Question 364073: What is the sum of the first eleven terms of the arithmetic sequence
3, 5 1/2 , 8, ...... ?
a 28 b 143 1/2 c 154 d 170 1/2 e 175

Click here to see answer by vasumathi(46)

Question 364094: What is the common ratio of the third term of a geometric progression is 360 the sixth term is 1215.
Click here to see answer by amoresroy(361)

Question 365094: Hi! I need some help developing a rule for the following number sequence: 4, 10, 18, 28, 40, 54, 72...
I know that the pattern is increasing by two each time, but I am struggling to find a rule for this pattern.
Any help would be appreciated!
Thanks!!
Click here to see answer by Fombitz(32388)

Question 366309: what is a number whose product with 3 is the same as its sum with 30
Click here to see answer by stanbon(75887)

Question 366489: If 3, 6, 12, 2y + 6 is a geometric sequence, what is the value of y?
Click here to see answer by Fombitz(32388)

Question 366893: can you show me the steps of working out, (-1)power n n divided by n+4 Un= 7/9

Click here to see answer by Fombitz(32388)

Question 367046: What is the 15th term of the sequence -13, -9, -5, -1, . . . ?
Click here to see answer by robertb(5830)

Question 367044: test for convergence of a series
1/1 + 4/4 + 9/27 + 16/256 +��

Click here to see answer by robertb(5830)

Question 367543: The first three terms in the binomial expansion of (1+ kx)n are 1− 21x +189x2.
Find the value of n and the value of k.
Please show all the steps etc... I know the answer, but I don't understand the solution at all... thanks
Click here to see answer by robertb(5830)

Question 367620: The first term of a geometric sequence is 5 and the third term is 7.2.Which of the
following can be the fifth term?
(A) 8.85 (B) 9.4 (C) 10.368 (D) 11.646 (E) 12.4416
Click here to see answer by robertb(5830)

Question 367883: Can you explain to me how to do explicit formulas in algebra 2?
Click here to see answer by Fombitz(32388)

Question 368338: This is a 5th grade math problem that I heard from a friend and I am curious to learn the answer.
A student has a test with 2 parts. Part A questions are worth 2 points and Part B are worth 5 points each. The student gets all the questions right in part A but misses 1 question in part B. The student scores an 85% on the overall test. How many questions are on the test? Help I tried to do:
2x__ +5x___ (-5) = .85 but I can't make it come out to 85%
Thanks for your help
Click here to see answer by stanbon(75887)

Question 368522: for the sequence 12, 15, 18, 21........
what is the equation to find the nth term of the sequence?
Click here to see answer by Fombitz(32388)

Question 368722: Find the nth term formula for the sequence 2,-1,-4,-7....
Click here to see answer by Fombitz(32388)

Question 369059: Is there a formula that might help me figure out sequences and the nth term
Click here to see answer by ewatrrr(24785)

Question 368945: 9, 19, 40, ?, 146
Click here to see answer by Edwin McCravy(20056)

Question 369238: on a map, the scale reads 1/4 inch = 10 miles. How many miles apart are two cities if the distance between them on the map is 2.5 inches?
A) 10
B) 25
C) 40
D) 100
E) 250
Click here to see answer by robertb(5830)

Question 369376: factor completely.
x squared + 2xy + 2x + y squared + 2y - 8
Click here to see answer by mananth(16946)

Question 370519: What is the answer to find the sum of the first 70 terms of the arithmetic sequence 45, 39, 33, 27?
Click here to see answer by stanbon(75887)

Question 370797: How would you change these two mixed numbers to improper fractions: 3 7/12, 1 6/13.
Click here to see answer by stanbon(75887)

Question 371140: A sequence goes 1,2,2,3,3,3,...
Find the 66th term. Please show all the steps and explain why it is like that

Click here to see answer by jim_thompson5910(35256)

Question 371452: Define the a₃ and a₄ terms of the recurrence relation:
a_n+2= 2a_n+1 - 3a_n where a₀ = a₁ = 3

Click here to see answer by Edwin McCravy(20056)

Question 371414: Find the sum of the first twenty terms of the sequence 3,5,7,........
Click here to see answer by ewatrrr(24785)

Question 371414: Find the sum of the first twenty terms of the sequence 3,5,7,........
Click here to see answer by jrfrunner(365)

Question 371626: find the slope of the line containing the points. (2,4) and (3,-5)
Click here to see answer by mananth(16946)

Question 372258: 5(7)(-9)
Click here to see answer by rfer(16322)

Question 372230: Luke started working in 1980 at an annual salary of $14,000 with a raise of $550 each subsequent year. Rachel started working at the same office in 1984 at an annual salary of $15000 with a raise of $700 each subsequent year. In what year will they earn the same salary?
Click here to see answer by r(2)

Question 372583: Can you please help me find the first five terms of the sequences with the nth term given as follows:
(a) 6n + 2 ________, ________, ________, ________, ________
(b) n� + n2 + 2n + 1 ________, ________, ________, ________, ________
(c) 2n + 3 ________, ________, ________, ________, ________

Click here to see answer by Fombitz(32388)

Question 373899: simplify the factorial (4n+2)!/(4n)! ; and given the folowing sequence 5+5/6, 5+7/8, 5+9/10, 5+11/12, 5+13/14,... write an expression for the apparent nth term assuming n begins with 1. Thanks
Click here to see answer by Fombitz(32388)

Question 374209: The sequence is defined recursively. Write the first four terms
a1 = 3; an = 3an-1 + 4
Click here to see answer by robertb(5830)

Question 374598: if 4Cr represents the number of combinations of n items taken r at a time, what is the value of sigma[1,3,[4Cr]? answers are: (1)24, (2)6, (3)14, (4)4.
where r=1
thank you in advance for your help.
Click here to see answer by jim_thompson5910(35256)

Question 375017: Find the sum of the infinite geometric series 8+8/3+8/9+8/27....
Click here to see answer by Fombitz(32388)

Question 375018: How many 10 digit numbers can be formed if the first three digits are 407?
Click here to see answer by Edwin McCravy(20056)

Question 375263: 1/8, 2/7, 1/2, 4/5 what are the next two terms?
Click here to see answer by jim_thompson5910(35256)

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