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 1025383: What is the pattern for
3, 1, 1/3, 1/9...
Click here to see answer by josgarithmetic(39617)

Question 1025393: Use S = n^2 to find the sum of 11 + 13 + ... 701
Click here to see answer by robertb(5830)

Question 1025556: Use mathematical induction to prove the statement is true for all positive integers n.
The integer n� + 2n is divisible by 3 for every positive integer n.
Click here to see answer by Edwin McCravy(20056)

Question 1025555: Find the sum of the first 8 terms of the sequence.
1, -3, -7, -11, ...
Click here to see answer by Emilym1234(10)

Question 1025555: Find the sum of the first 8 terms of the sequence.
1, -3, -7, -11, ...
Click here to see answer by MathTherapy(10552)

Question 1025533: Find the general term
(1,1/3,-1/6,1/10,-1/15,1/21,....)
Click here to see answer by robertb(5830)

Question 1025524: Given the geometric sequence: 27,270/7,2700/49...

Please help me. The answers I got is wrong. What am I doing wrong
Find an explicit formula for an.

a_n=27(10/7)^n(n-)

Find a_9=27000000000/403500000

Click here to see answer by robertb(5830)

Question 1025527: Please help me I have enclosed my answers also that I got but part B is wrong.
Write the sum using sigma notation:
1+2+3+4+⋯+102=
A
∑ B
n=1, where
A=102

B=1/n+1

Click here to see answer by rothauserc(4718)

Question 1025553: certain species of tree grows an average of 0.5 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 800 centimeters tall.
Click here to see answer by Alan3354(69443)

Question 1025557: A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.
Click here to see answer by Alan3354(69443)

Question 1025554: A certain radioactive isotope has a half-life of 15 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?
Click here to see answer by josgarithmetic(39617)

Question 1025676: Please help me I came up with the first answer.

Write the sum using sigma notation:
1+2+3+4+⋯+102=
A
∑ B
n=1

Click here to see answer by ikleyn(52787)

Question 1025788: find the real number solution of |2x-3|< or = 10

Click here to see answer by josgarithmetic(39617)

Question 1025935: Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false.
1. 4 ⋅ 6 + 5 ⋅ 7 + 6 ⋅ 8 + ... + 4n( 4n + 2) = 4(4n+1)(8n+7)/6
2. 1^2 + 4^2 + 7^2 + ... + (3n - 2)^2 = n(6n^2-3n-1)/2
Click here to see answer by Edwin McCravy(20056)

Question 1025864: find the formula for the nth term of the sequence: 60, 48, 38, 30, 25

Click here to see answer by josgarithmetic(39617)

Question 1025964: How many consecutive integers beginning with 5 must be taken for the sum to equal 95.

Click here to see answer by FrankM(1040)

Question 1025992: Find the five numbers in A.P Whoes sum is 55 and sum of whoes square is 765?
Click here to see answer by Fombitz(32388)

Question 1026099: Write the sum using summation notation, assuming the suggested pattern continues.
8 - 40 + 200 - 1000 + ...
Click here to see answer by ikleyn(52787)

Question 1026097: Write the sum using summation notation, assuming the suggested pattern continues.
-4 + 5 + 14 + 23 + ... + 131
Click here to see answer by ikleyn(52787)

Question 1026095: Write the sum using summation notation, assuming the suggested pattern continues.
25 + 36 + 49 + 64 + ... + n^2 + ...
Click here to see answer by ikleyn(52787)

Question 1026132: Use mathematical induction to prove the statement is true for all positive integers n.
The integer n^3 + 2n is divisible by 3 for every positive integer n.
please show work so I can understand it:)

Click here to see answer by ikleyn(52787)

Question 1025981: What are the missing numbers in this sequence:
6-2-1-3-?-?-4
Click here to see answer by ikleyn(52787)

Question 1026123: find the next two term in the following series. 4,6,8,12,14,18,20,24,30,?,?,

Click here to see answer by Edwin McCravy(20056)

Question 1026195: Tell whether the sequence is arithmetic. If it is identify the common difference.
Thank You for helping me. If you can.
0, 1/3, 2/3, 1,....

Click here to see answer by richard1234(7193)

Question 1026310: what is the next # in the sequences below
3, -6, 12, 4, 20, ?
7, 16, 8, 27, 9, ?
2, 7, 26, 101, 400?
7, 21, 8, 72, 9
Click here to see answer by ikleyn(52787)

Question 1026197: write the first seven terms, the 20th term, and the sum of the first 20 terms for the arithmetic sequence where a =1 and d=2.5
1
Click here to see answer by mananth(16946)

Question 1025111: Please help me, Thanks
Write the sum using sigma notation:
1+2+3+4+⋯+102=
A
∑ B
n=1 where
A=
B=
Click here to see answer by Edwin McCravy(20056)

Question 1025107: Please help me

Given the geometric sequence: 33,12/1,48/11...

Find an explicit formula for an.
a_n=

Find a_10=

Click here to see answer by Edwin McCravy(20056)

Question 1026504: How do I put -13+(-26)+(-39)+(-52)+(-65)+(-78) into sigma not�tion?
Click here to see answer by josgarithmetic(39617)

Question 1026557: find the next term 1,7,47,?
Click here to see answer by rothauserc(4718)

Question 1026557: find the next term 1,7,47,?
Click here to see answer by Edwin McCravy(20056)

Question 1026557: find the next term 1,7,47,?
Click here to see answer by Alan3354(69443)

Question 1026638: Find the missing number
2 8 9 31
1 3 2 11
3 7 5 28
5 2 3 ?
How to solve it......plz tell me Sir
Click here to see answer by robertb(5830)

Question 1026663: Find the coefficient of 𝑥5𝑦11 in the expansion of (2𝑥 − 𝑦)16.
Click here to see answer by robertb(5830)

Question 1026662: 100
Σ
k=2(𝑘 − 1)(𝑘 + 1)
Click here to see answer by ikleyn(52787)

Question 1026751: 1. Five cards are chosen from a random a standard deck of playing cards. In how many ways can the cards be chosen under each of the following condition.
a.) all are hearts. b.) Exactly three kings
2. Use mathematical induction to prove 2+2+8+..+2^n= 2(2^n -1)
THANK YOUUUUU.
Click here to see answer by Edwin McCravy(20056)

Question 1026868: complete the series 22,18,27,16,23

Click here to see answer by robertb(5830)

Question 1026868: complete the series 22,18,27,16,23

Click here to see answer by ikleyn(52787)

Question 1027136: Please need help. Thanks all the tutors here.
Determine the first 5 susesion terms of:
an=2n+5

Click here to see answer by stanbon(75887)

Question 1027204: What is similarity between 85.17.19.4and2?
Click here to see answer by Alan3354(69443)

Question 1027329: Write a recursive formula for the sequence 40, 20, 10, 5, 5/2 then find the next term
Click here to see answer by Boreal(15235)

Question 1027358: Find the function (rule) that describes the sequence 6, 12, 18, 24, and find the next three in the sequence.
My answer:
The rule is y = 6x , the next three are 30, 36, 42
is this correct? please help
Click here to see answer by josgarithmetic(39617)

Question 1027356: Find a function (rule) that describes the sequence" 24, 21, 18, 15 and find the next three in the sequence.
Click here to see answer by josgarithmetic(39617)

Question 1027441: Thanks for your help, Have no idea
Determine the first 5 susesion terms of:
Bn=(-2)^(n-1)
Click here to see answer by fractalier(6550)

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