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 196951: Find the arithmetic mean an of the given terms.
1. an-1=0,an+1=5
2. an-1=2/3,an+1=4
Click here to see answer by stanbon(75887)

Question 196965: Given each set of axes, what does the area under the curve represent?
48. y-axis: feet per second^2; x-axis: seconds
49. y-axis: dollars per pound; x-axis: pounds
50. y-axis: calories per ounce; x-axis: ounces
Click here to see answer by RAY100(1637)

Question 197716: sum[n-3,6,1/2n]
A - 19/2
B - 9
C - 6
D - 12
I reread my textbook and have tried trial-and-error and the process of elimination.
Click here to see answer by user_dude2008(1862)

Question 198172: This is from a worksheet from K12-OHVA- My internet school.
How do I find the sum of this finite geometric series? I will use an E for the Sigma notation.
8
E <-1/2)^i-1
i=1

Thank you
Click here to see answer by stanbon(75887)

Question 198207: Worksheet from my school OHVA
Find the sum of the arithmetic series
1+14+27+...+183
Thank you!
Click here to see answer by arallie(162)

Question 198323: Worksheet from school
Find the explicit and recrusive formula for the sequence:
10, 15, 20, 25, 30,...
and
1,4,9,16,25,36,49,...
Click here to see answer by user_dude2008(1862)

Question 198208: For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
1. 1+4+7+...; S8
2. 1+4+16+...; S8
3. 288+144+72+...; S7
4. 42+55+68+...; S12
5. -20-12-4+4+...; S10
6. 2-6+18-54+...; S10

Click here to see answer by arallie(162)

Question 198321: Worksheet from school-OHVA
Find the explicit formula for the following sequences:
123, 116, 109, 102, 95,...
and
1/6, 1/12, 1/24, 1/48, 1/96,...
Click here to see answer by user_dude2008(1862)

Question 198372: the product (1- 1/2)(1- 1/3)(1- 1/4) (1-1/5)�(1-1/99)(1-1/100) is equal to
a) 1/99 b) 1/80 c) 1/90 d) 1/100 e) none of these

Click here to see answer by jim_thompson5910(35256)

Question 198400: For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
4. 42+55+68+...; S12
5. -20-12-4+4+...; S10
6. 2-6+18-54+...; S10

Click here to see answer by arallie(162)

Question 198399: For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
4. 42+55+68+...; S12
5. -20-12-4+4+...; S10
6. 2-6+18-54+...; S10

Click here to see answer by arallie(162)

Question 198398:

For questions 1-6 determine whether each series is arithmetic or geometric. Then evaluate the series to the given term.
1. 1+4+7+...; S8
2. 1+4+16+...; S8
3. 288+144+72+...; S7

Click here to see answer by arallie(162)

Question 199031: addition of 1*1+2*2+3*3+......+50*50
Click here to see answer by solver91311(24713)

Question 199203: What is the equation to the problem twice the square of a number is the same as eight times the same number
Click here to see answer by Alan3354(69443)

Question 199680: Find the x values so that the infinite series become finite.
(infinite)
(Sigma) 3(x-2)^(k-1)
(k=1)
Could you help me with this question? Thank you.
Click here to see answer by jim_thompson5910(35256)

Question 199771: Hello and Thank You for your help.
I know the answewr to my problem is 10 years. I kept subtracting to get the answer. I don't know how to write an equation to solve the problem. The question is
Bill will put aside $100 per month this year for retiremenmt. Next year he will put away $200 per month the third year $300 per month. Each year will increase by $100 per month. How many years will Bill save to reach $66,000?
Click here to see answer by jim_thompson5910(35256)

Question 199910: the sum of a series with a set of 1+5+10+25+50
Click here to see answer by jim_thompson5910(35256)

Question 199930: I want to know the difference between a sequence and a progression. Are these two different from a pattern? Can you cite some examples. Is 1,11,111,1111,.... a sequence or a pattern. Are all sequences patterns or it is the other way.Similarly are all sequences progressions or it is the other way.
Click here to see answer by Edwin McCravy(20056)

Question 200754: state the next number in the sequence 1,1,1,2,2,3,3,4,5,5,8,6,13,7,21,8,34,9,_
Click here to see answer by jim_thompson5910(35256)

Question 200896:
4,2,8,4,12,6,?
Click here to see answer by rfer(16322)

Question 201375: The middlepoints of the side of a triangle are joined forming a second triangle.Again a third triangle is formed by joining the middles points of this second triangle and this process is repeated infinitely.If the perimeter and area of the outer triangle are P and A respectively,What will the sum of perimeters of the triangles thus formed?
Click here to see answer by solver91311(24713)

Question 201610: which is the 9th term of the sequence which has a first term of 1 and has a common ratio of 1.5
Click here to see answer by RAY100(1637)

Question 201609: which is the 9th term of the sequence which has a first term of 1 and has a common ratio of 1.5
Click here to see answer by RAY100(1637)

Question 201608: find the 6th term of the sequence which has a first term of 5 and has a common ratio of 4.2
Click here to see answer by RAY100(1637)

Question 201734: use the factor theorem to determine whether (x-3) is a factor of f(x)=X^4+12x^3+6x+27.
Click here to see answer by stanbon(75887)

Question 201907: Please Help:
Find the sum of the first five terms of the geometric sequence.
a = 5, r = 4
A) 1715
B) 1704
C) 1701
D) 1705

Click here to see answer by nerdybill(7384)

Question 201907: Please Help:
Find the sum of the first five terms of the geometric sequence.
a = 5, r = 4
A) 1715
B) 1704
C) 1701
D) 1705

Click here to see answer by jim_thompson5910(35256)

Question 201924: Please Help:
Find the indicated term of the geometric sequence.
a = -3, r = -4; Find the 7th term.
A) 3072
B) 196,608
C) -4096
D) -12,288

Click here to see answer by jim_thompson5910(35256)

Question 201898: Please Help:
Find the sum of the first five terms of the geometric sequence.
a = 1, r = 2
A) 31/5
B) 91/3
C) 31
D) 91/15

Click here to see answer by jim_thompson5910(35256)

Question 201897: Please Help:
Find the sum of the first five terms of the geometric sequence.
a = 1, r = 2
A) 31/5
B) 91/3
C) 31
D) 91/15

Click here to see answer by jim_thompson5910(35256)

Question 201893: Please Help:
Find the sum of the first five terms of the geometric sequence.
a = 1, r = -3
A) 121
B) 61
C) -121
D) -61

Click here to see answer by jim_thompson5910(35256)

Question 202544: Can ANYONE help me with these two problems? Please!

Type the general term for the following sequences:

#1) 3, 9, 27, 81, 243, . . .
__________

#2) 3/4, 6/5, 9/6, 12/7, 15/8...
__________

Thanks,
Sarah
Click here to see answer by jim_thompson5910(35256)

Question 202838: Algebra 2 worksheet on Arithmetic sequence
The third term of an arithmetic sequence is 9 and the seventh term is 31. Find the sum of the first twenty-two terms.

How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762?

Click here to see answer by Edwin McCravy(20056)

Question 203033: Hi i would like help on geometric Sequences.
The Question says Find the common ratio of a geometric sequence which has a first term of 5 and a sum to infinity of 6.
The sum to infinity equation is S"infinity"=(a)/(1-r)
so i changed the a to a 5 and made it equal to 6 so the equation was 6=(5)/(1-r) the answer is 1/6 but i keep getting 5/6 can you please help
Thanx
Peder
Click here to see answer by vleith(2983)

Question 203130: What is the next sequence of numbers; given: 4,18,200,20402
Click here to see answer by vleith(2983)

Question 203569: Can someone please help me with this problem:
Find the indicated term of the geometric
sequence.
, ; Find the 8th term.
Click here to see answer by Edwin McCravy(20056)

Question 203582: find a quadratic equation with roots (4+i) and (4-i)
Click here to see answer by stanbon(75887)

Question 203557: A sequence starts with the term 2222. Each succeeding term is found by adding 1010 to the previous term. What is the sum of the sixth and seventh terms?
Click here to see answer by scott8148(6628)

Question 203583: I need help with this problem, please help me:
i need to find the positive root, negative roots, and rational roots.
Given x^3-4x^2+2x+1=0

i got for the positive root=2
negative root=1
and im having trouble finding the rational roots.
thank you in advance!

Click here to see answer by stanbon(75887)

Question 203816: how many integers between 26 and 415 are multiples of 9?
please help. thank you :)
Click here to see answer by RAY100(1637)

Question 204302: Is the following sequence arithmetic or geometric?
1/2, 1/10, 1/50, 1/250, 1/1250...
Find the common difference or ratio depending on your decision to the first part of the question.

Click here to see answer by RAY100(1637)

Question 204345: Find the sum of the infinite series:
∞
∑ (3/2^i+4/5^i)
i=1
So far I know that it goes: 23/10, 91/100, 407/1000, etc., in multiples of ten for the denominator, but I am confused as to what the top sequence is and if it's supposed to go to infinity, and then how would I find the sum?
Thank you in advance
Click here to see answer by jim_thompson5910(35256)

Question 204545: Find the first five terms of the sequences with the nth term given as follows:

Click here to see answer by alicealc(293)

Question 204792: Find the first 5 terms
an=1/n^2
Click here to see answer by Earlsdon(6294)

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