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 391334: How would you continue the following number sequence? and Why?
100, 101, 103, 107, 115, 122, 127, ...
Click here to see answer by Alan3354(69443)

Question 391314: how do you find the avarage mean of the following data.
42 62 78 90 110 120
Click here to see answer by Alan3354(69443)

Question 391704: The table shows the cost of buying mugs. Write an equation to model the data, Explain how you arrived at you equation.
Number of mugs 1, 2, 3, 4, 5
Total cost 11, 18, 25, 32, 39
you must include both the equation and explanation in your response.
Click here to see answer by Edwin McCravy(20056)

Question 391759: if the first term of a geometric sequence is 3/2 and the second and third terms are -3/4 and 3/8, respectively, which of the following represents the nth term of the sequence?
a) 3(-1)^n-1/2n
b) 3(-1)^n/2n
c) 3(-1)^n-1/2^n
d) 3(-1)^n/2^n
e) 3(-1)^n-1/2^n+1
please provide explanation!
Click here to see answer by stanbon(75887)

Question 391969: Find the distance between points at (4,-1) and (-2,-5).
Thank you so much for all of your help!!!!!!
God Bless!!!!!!
Click here to see answer by Edwin McCravy(20056)

Question 392147: 150,30,6,.....
in the sequence above , each term after the 1st term is 1/5 of the term preceding it.what is the 5th term of this sequence ?
Click here to see answer by robertb(5830)

Question 392679: A geometric sequence has all positive terms. The sum of the first two terms is 15 and the sum of infinity is 27. Find the value of
(a) The common ratio;
(b) The first term;
Thank you :)
Click here to see answer by ewatrrr(24785)

Question 392874: what are the next two terms for 5000, 2000, 200, 40 ...
Click here to see answer by MathLover1(20850)

Question 392911: Write an algebraic expression for the following sequence 2, 4, 8, 14, 22, 32, ....
Click here to see answer by robertb(5830)

Question 392971: What is the 12th term and rule of 2,-6,18,-54,162
Click here to see answer by robertb(5830)

Question 393587: Can you please help me solve this question:
What are three consecutive even integers whose sum is -12 ?
Click here to see answer by ankor@dixie-net.com(22740)

Question 393639: Find the fraction which is equivalent to 0.015 (reoccurring)
This question is driving me nuts,please help
Click here to see answer by Alan3354(69443)

Question 393642: Use mathematical induction to prove that
1^3+2^3+3^3+....+n^3=(1+2+3+....+n)^2
Please I need your assistance
Click here to see answer by richard1234(7193)

Question 393978: I have to find the Recursive Definition for the sequence 0,3,7,12,18...
I have tried several different ways of writing the formula but none worked. The closest i got was 〖〖(A〗_(n-1))〗^2 +3.
when inputting this it worked for all A's except A_5 which gave me 19 instead of 18. :( somebody please help.
Please and thank you :)

Click here to see answer by richard1234(7193)

Question 393636: For the series 64,-32,16,-8 find:
i)The tenth term
ii)the sum of the first 20 terms
iii)the sum to infinity
Please help I have already done the first two questions with the results of:
i)0.0625
ii)-127.99 (rounded)
But I am stumped for the third question.
Click here to see answer by richard1234(7193)

Question 394655: Please help me, Im having so much trouble with this question.
Use Pascals triangle to expand (x-7)^5
Click here to see answer by josmiceli(19441)

Question 394654: If the third term of an arithmetic sequence is 14 and the eighth term is -1, find the values of a1 and d of the sequence.

Click here to see answer by ewatrrr(24785)

Question 394635: if 12 is added to this product, the result is 147 find the number
Click here to see answer by ewatrrr(24785)

Question 394739: A pizza shop advertises that they have 8 toppings, and they sell large, medium, and small pizzas. On a small pizza, you must choose 3 different toppings. On a medium pizza, you must choose 4 different toppings, and on a large, you must choose 5 different toppings. How many different pizzas can they make?
choose the answer and explain the reason to choose your response, the answer has to be one of the following:
475
219
182
657

Click here to see answer by ewatrrr(24785)

Question 395408: Hello,
What is the 6th number of the next series? and why?
1,4,9,36,41, ....
Thank you very much!

Click here to see answer by jim_thompson5910(35256)

Question 395408: Hello,
What is the 6th number of the next series? and why?
1,4,9,36,41, ....
Thank you very much!

Click here to see answer by Edwin McCravy(20056)

Question 395380: find the 100th and nth term for each of the sequences:
a. 8,11,14,17,20,...
b. 1,16,81,256,625,...
c. 5,15,45,135,405,...
d. 2,7,12,17,22,...
e. 1,1/2,1/4,1/8,1/16,...
Click here to see answer by robertb(5830)

Question 395978: Using the following six digits, 1, 2, 4, 6, 8, and 9, fill in the blanks below to make the maximum product that you can. Use each digit only once. How does an understanding of place value help determine the best solution to this problem?

Click here to see answer by Edwin McCravy(20056)

Question 396463:
The table shows Cassie's age and Heather's age over 3 consecutive years. Cassie's age, x (years) Heather's age, y (years) 12 15 13 16 14 17 15 18 Which expresion can be used to represent Heather's age in terms of Cassie's age?

Click here to see answer by Edwin McCravy(20056)

Question 396669: Write 2 - 4 + 8 - 16 + ... + 128 using sigma notation.
Click here to see answer by ewatrrr(24785)

Question 396669: Write 2 - 4 + 8 - 16 + ... + 128 using sigma notation.
Click here to see answer by CharlesG2(834)

Question 396693: What is the formula for sum{i} [i chnages from i=a to i=n] where a is an integer between 1 and n
Click here to see answer by CharlesG2(834)

Question 397019: Evaluate each expression -5!
Click here to see answer by richard1234(7193)

Question 398318: Sequence us 1, 8, 27, ?, 125, 216
What is missing number. Driving me crazy. Can't figure out pattern.
Click here to see answer by Alan3354(69443)

Question 398922: Find S8 for the geometric series 256 + 64 + 16 + 4 +�
Click here to see answer by Theo(13342)

Question 398942: Find the 8th term in the geometric sequence with t4 = 48 and t6 = 192.
Click here to see answer by ewatrrr(24785)

Question 399240: Find the sum of the following infinite geometric series, if it exists.
1.02 + 2.04 + 4.08 + 8.16 +�
Click here to see answer by richard1234(7193)

Question 399240: Find the sum of the following infinite geometric series, if it exists.
1.02 + 2.04 + 4.08 + 8.16 +�
Click here to see answer by robertb(5830)

Question 399540: in an arithmetic sequence, a3=-8 and a17=48
find the 20th term for the sequence
Click here to see answer by ewatrrr(24785)

Question 399540: in an arithmetic sequence, a3=-8 and a17=48
find the 20th term for the sequence
Click here to see answer by rahulsoni001002(1)

Question 400332: what is fifth term of a sequence whose first term is 8 and common ration is 3/2
Click here to see answer by robertb(5830)

Question 401429: if the 3rd term of a G.P. is the square of its first term and its 5th term is 64, find its first term and the common ration.
Click here to see answer by robertb(5830)

Question 402481: Josie says that s=n/n+1 and s/1-s=n are two ways to write the same formula. do you agree or disagree with Josie? Explain
Click here to see answer by stanbon(75887)

Question 403038: Please explain how (square root 5 + square root 5)2 is larger than 5 +
5square root 5. Sorry,there is no square root sign on the keyboard.
Click here to see answer by MathLover1(20850)

Question 403194: how to slove recursive addition sequences: 3,_,_,_,21
_,0_,_,_,-3
7,_,_,_,2
0,_,_,_,_,_,3
Click here to see answer by the_hustle07(1)

Question 403470: what is the next term in the sequence below?
1, 8, 27, 64.....
Click here to see answer by Alan3354(69443)

Question 403601: find the 20th term of the arithmetic sequence 17,13,19
Click here to see answer by Edwin McCravy(20056)

Question 403728: Hi am slightly stuck on this question on number theory. I have solved it up to a point but don�t know how to get the values of (a, b, c)
Question. If abc + abc = cba in the scale of five (when abc means 5�a + 5b + c) find the values of a, b, c
Solution so far
Since the numbers are in the base 5 abc+abc=cba means
(25a+5b+c) + (25a+5b+c) = 25c+5b+a
Solving gives: 50a+10b+2c = 25c+5b+a
49a+5b = 23c
This is where I am stuck how do we find the values of a,b,c do we SOLVE or do we use trial and error and is there another method for solving the equation, which would give us the same answer.
The answer for a, b, c is given as 1, 4, 3
Ps the numbers are in the scale of five.
Thanks moses.

Click here to see answer by Alan3354(69443)

Question 404050: consider the following infinite sequence of numbers 17, 24, 31, 38, 45, 52. what is the least term in the sequence that is a multiple of 2, 3, 4, 5, 6?
Click here to see answer by Edwin McCravy(20056)

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