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 1090241: how do you find a pattern in a non linear functions?
Click here to see answer by dennisrizelleruiz(5)

Question 1090420: Relation between series 1,-3,5,-7,9...
Click here to see answer by Edwin McCravy(20056)

Question 1090598: The sum to infinity of a geometric sequence is 27/2 while the sum of the first three terms is 13. Find the sum of the first 5 terms.
Thank you for your help.
Click here to see answer by ikleyn(52788)

Question 1090634: Find the average of the middle 80% of the following series: 3, 7, 39, 41, 57, 84, 91, 95, 110, 144
Click here to see answer by Fombitz(32388)

Question 1090712: Find the nth term of the series 3 7 14 27 52
Click here to see answer by Edwin McCravy(20056)

Question 1090838: Can someone help me?
An amphitheater is set up so that there are 10 seats in the first row, 13 seats in the second row, 16 in the third row, 19 in the fourth row, etc., until there are 85 seats in the last row of the amphitheater.
a. how many rows are in the amphitheater?
b. How many total seats are in the amphitheater?
Thanks

Click here to see answer by ikleyn(52788)

Question 1090865: Solve the series
5 10 15 34 60 61 ?
Click here to see answer by greenestamps(13200)

Question 1090885: Can someone help me?
A sequence {g n} is defined recursively as g 1=72, g n=-2/3*g n-1 , for n ≥2
(note: here "n" & "1"& "n-1" after "g" should be a smaller letter, I cannot put it here as smaller)
a. Determine the values of g 2, g 3, and g 4
b. Write an explicit formula for g n
Thank you.
Click here to see answer by KMST(5328)

Question 1090876: 1,3,8,26,106,?
What will be the next number of the series and how?
Click here to see answer by Edwin McCravy(20056)

Question 1091192: What is the next set of numbers in sequence
3128,3130,3130,????
Click here to see answer by ikleyn(52788)

Question 1091240: what is the 45th term of a sequence generated by the formula tn=(-1)^n*(2n/2n+1)?
Click here to see answer by ikleyn(52788)

Question 1091239: what is the 45th term of a sequence generated by the formula tn=(-1)^n*(2n/2n+1)?
Click here to see answer by ikleyn(52788)

Question 1091274: Write down a recursive definition of the geometric sequence that has 1st term a and common ratio r.
Click here to see answer by ikleyn(52788)

Question 1091273: How do you find the two possible fourth values of a geometric sequence. There are two geometric sequences with 3rd term 5 and 5th term 80. What are the possible 4th terms?
Click here to see answer by ikleyn(52788)

Question 1091272: List the first six terms of the sequence defined by bn= (2*4*6 �2n)/2^n.

Click here to see answer by ikleyn(52788)

Question 1091027: A rubber ball is dropped on a hard surface from a height of 80 feet and bounces up and down. On each rebound, it bounces up exactly one-half the distance it just came down. How far will the ball have traveled if you catch it after it reaches the top of the seventh bounce?
*This is a Geometric Series question.
Click here to see answer by Edwin McCravy(20056)

Question 1091303: Insert 6 arithmetic means between 12 and 75
Click here to see answer by Edwin McCravy(20056)

Question 1091331: 248,241,244,122,115,118,59,?
Click here to see answer by math_helper(2461)

Question 1091331: 248,241,244,122,115,118,59,?
Click here to see answer by greenestamps(13200)

Question 1091469: Find the sum of the series 101+99+97+....+47.

Click here to see answer by ikleyn(52788)

Question 1091492: if a,b,c are in AP, aalnd a,mb,c are in GP then a, m^2b, c are in HP
Click here to see answer by MathLover1(20850)

Question 1091574: Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 4 + 1 + 6 + ... + 66
Click here to see answer by math_helper(2461)

Question 1091579: The difference between two positive numbers is 18 and 4 times their GM is equal to 5 times their HM find the numbers
Click here to see answer by rothauserc(4718)

Question 1091579: The difference between two positive numbers is 18 and 4 times their GM is equal to 5 times their HM find the numbers
Click here to see answer by ikleyn(52788)

Question 1091590: The sum of two conservative even integers is less than 84. Find the pair with the greatest sum.
Click here to see answer by MathLover1(20850)

Question 1091590: The sum of two conservative even integers is less than 84. Find the pair with the greatest sum.
Click here to see answer by MathTherapy(10552)

Question 1091590: The sum of two conservative even integers is less than 84. Find the pair with the greatest sum.
Click here to see answer by ikleyn(52788)

Question 1091588: If r varies jointly as s and t, and r=90 when s=8 and t=15, find r when s=7 and t=12
Click here to see answer by Boreal(15235)

Question 1091614: 1/(2+x)^4 modulus x >2
Click here to see answer by ikleyn(52788)

Question 1091490: if a,b,c are in AP, aalnd a,mb,c are in GP then a, m^2b, c are in HP
Click here to see answer by Edwin McCravy(20056)

Question 1091658: 5,2,8,3,11,4,14,5,17,6,...
Click here to see answer by greenestamps(13200)

Question 1091656: Please help. How do I graph the sequence?
d n= 3+2n (n after "d" should be smaller)
Thank you.
Click here to see answer by MathLover1(20850)

Question 1091635: Expand. ( 2 + x )^(-4) where |x|>2
Click here to see answer by Edwin McCravy(20056)

Question 1091746: Find the sum of the first 30 terms of the arithmetic sequence : 10,5,0,-5
Click here to see answer by Boreal(15235)

Question 1091746: Find the sum of the first 30 terms of the arithmetic sequence : 10,5,0,-5
Click here to see answer by MathTherapy(10552)

Question 1091742: 1,5,3,7,5,9,7 next #

Click here to see answer by MathLover1(20850)

Question 1091745: Write a formula for the nth term of the infinite sequence. Do not use a recursion formula 4,16,64,256,1024
Click here to see answer by ikleyn(52788)

Question 1091771: Consider a geometric sequence whose third term is
9 and whose sixth term is −8/3. What is its first term?
(Enter a number only)
Click here to see answer by ikleyn(52788)

Question 1091771: Consider a geometric sequence whose third term is
9 and whose sixth term is −8/3. What is its first term?
(Enter a number only)
Click here to see answer by MathTherapy(10552)

Question 1091756: Please help...
If {b n} is an arithmetic sequence, explain why {10^bn} must be geometric.
Thank you.
Click here to see answer by ikleyn(52788)

Question 1091784: Insert the missing number 5,11,21,43
a)85 b) 86 c)87 d) 88
Click here to see answer by greenestamps(13200)

Question 1091741: Please help.
The population of town was 525,000 in 1992 and is growing annually at the rate of 1.75%. Write a recursive sequence Pn for the population. State the first term P1 for the sequence.
I tried to solve...
It is geometric sequence, I think.
So, An=A n-1*r (n & n-1 is smaller letter)
Pn=P n-1 *(0.0175) This is recursive sequence for Pn.
Then how do I state the P1?
Thank you.
Click here to see answer by Theo(13342)

Question 1091788: how many terms of the series -9,-6,-3, ....will be 66?
Click here to see answer by Fombitz(32388)

Question 1091854: How do I find out the limit of this equation?
n goes towards infinity and starts at zero. It didnt look nice when I tried to
write it in the equation

Click here to see answer by math_helper(2461)

Question 1091859: Please help...
I know the arithmetic sequence Sn=n(A1+An)/2, but I cannot solve this problem
Q: nth triangular number = n(n+1)/2,
Prove this formula algebraically using the sum of a finite arithmetic sequence theorem.
Thank you.
Click here to see answer by math_helper(2461)

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