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 1100442: 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 Shin123(626)

Question 1116401: Use the explicit formula an = a1 + (n - 1) � d to find the 500th term of the sequence below.
24, 30, 36, 42, 48, ...
Click here to see answer by ikleyn(52787)

Question 1116519: What is the sum of the first five terms of the series 35 + 30 + 25 +... ?
Click here to see answer by josgarithmetic(39617)

Question 1116497: what is the next term
4,7,25,10_,20,16,19
Click here to see answer by ikleyn(52787)

Question 1116659: A sequence is formed by adding corresponding terms of an A.P. and a
G. P., with r = 2, The first, second and third terms of the sequence are 3,7
and 12 respectively. Find the A.P. and the G.P., and give an expression for
the sum of the first n terms of the sequence.

Click here to see answer by greenestamps(13200)

Question 1116740: Please help me with this problem: Resolve into infinite series
I can't show how I tried on this problem because it is very complicated! I did try several times though.
This is the answer from my key book: x+x^2/a+x^3/a+x^4/a,ect., to infinity
I don't understand how the fractions are able to keep repeating. When I worked the problem I got as far as x+x^2/a, but no farther.
I appreciate any help you can offer!
Click here to see answer by Edwin McCravy(20056)

Question 1116961: 2,24,46 ... Find the 25th term
42,32,22,12 ... Find the 35th term
3,-18,108,-648 ... Find the 22nd term
2,1,1/2,1/4 ... Find the 9th term
Someone please help me with these? I need this worksheet done asap

Click here to see answer by stanbon(75887)

Question 1116967: Someone please help me with this, been at this worksheet for hours and need it done ASAP

Identify the sequence (If it does not fit any of the 4 sequences, give reasons behind why it doesn�t work)
13,21,34,55,89,144 ...
4,-2,-8,-14 ...
2,10,15,22 ...
3,18,108,648 ...
169,196,225,256 ...
Click here to see answer by stanbon(75887)

Question 1116977: Compute the sum and enter your answer as a common fraction:
1.11111111... + 0.11111111... + 0.01111111... + 0.00111111... + 0.00011111... + 0.00001111... + 0.00000111... + ....

Click here to see answer by ikleyn(52787)

Question 1116978: Determine all nonnegative integers r such that it is possible for an infinite geometric sequence to contain exactly r terms that are integers. Prove your answer.
Click here to see answer by KMST(5328)

Question 1116991: A rubber ball gets dropped on a hard surface, taking a sequence of bounces that are 3/5 as high as the preceding one. If the ball is dropped from 10 feet, what is the total vertical distance it has traveled after it hits the surface the 5th time?
Click here to see answer by rothauserc(4718)

Question 1117070: A clock pendulum swings through an arc of 30cm. Each successive swing is 10% less. How far will the pendulum swing altogether before coming to a complete stop?
The answer is 300cm.
I am not sure how to do the question above.

Click here to see answer by ikleyn(52787)

Question 1117069: A clock pendulum swings through an arc of 30cm. Each successive swing is 10% less. How far will the pendulum swing altogether before coming to a complete stop?
The answer is 300cm.
I am not sure how to do the question above.

Click here to see answer by ikleyn(52787)

Question 1117074: Seventy two grams of fertilizer is given to a dogwood tree the first year, 60 grams the second year, 50 grams the third year, and so on. Find the total amount of fertilizer received by the dogwood tree.
The answer is 432
I don't know how to do this.
Click here to see answer by ikleyn(52787)

Question 1117078: A ball from 10m above ground rebonds 3/4 of the distance from where it fell.
a) Find the total vertical distance the ball travels before coming to a rest. (Answer: 70m)
b) Find the total vertical distance the ball travels after 10 bounces. (Answer: 65.495)
c) What is the total distance traveled after the 10th bounce? (Answer: 4.505m)
I am not sure how to do them
Click here to see answer by Boreal(15235)

Question 1117129: What is the nth term of the sequence below?
�5,�7,�9,�11,�13

Click here to see answer by Alan3354(69443)

Question 1117124: Find the following:
a. the 25th term in the arithmetic sequence given that a1 = 4 and a2 = 9
b. the sum of the first 60 terms of the arithmetic sequence 4, 7, 10, 13, ......
Click here to see answer by greenestamps(13200)

Question 1117125: Find the following:
a. the 11th term in the geometric sequence given that a1 = -3 and a2 = 9
b. the sum of the first 10 terms of the geometric sequence 5, 15, 45, ....
Thank you!
Click here to see answer by stanbon(75887)

Question 1117244: Find the 110th term of the sequence -7, 3, 13, 23
A) 1,083
B) -1,097
C) 1,093
D) 40
By logic, I can already rule out B and D but am not sure how to figure out the answer between A and C.
Click here to see answer by ikleyn(52787)

Question 1117243: Find the 50th term of the sequence: 5, -2, -9, -16
A) -352
B) -343
C) -338
D) -331
Click here to see answer by ikleyn(52787)

Question 1117261: What is the 100th term of the sequence with a1 = 222 and d = -5
Click here to see answer by greenestamps(13200)

Question 1117305: Consider the infinite geometric series (linked below). In this image, the lower limit of the summation is "n=1".
As I am not sure how to type this in formatting on this website or how to type this in text this is a link to an image of the formula mentioned above.
https://postimg.cc/image/hchcwn7jr/
A) Write the first four terms of the series.
B) Does the series diverge or converge?
C) If the series has a sum, find the sum.
Click here to see answer by rothauserc(4718)

Question 1117385: Write a recursive definition for the sequence 11, 8, 5, 2,...
a1=11, an=an-1-4
a1=11, an=an-1-3
a1=2, an=an-1-3
a1=2, an=an-1+3
Much of that is meant to be in subscript, however, I don't know how to do subscript on here and couldn't get it to copy paste over, here is a photo, I do apologize that the entire problem can't be seen on here.
Here is the photo of the four answers with subscript. https://postimg.cc/image/sszribopz/
Click here to see answer by stanbon(75887)

Question 1117386: Write an explicit formula for the sequence -3, 1, 5, 9,...
A) an=-3+4(n-1)
B) an=-3+4n
C) an=-3+(n-1)
D) an=-3+4(n+1)
The "n" of "an" is meant to be in subscript but nothing else is.
Click here to see answer by stanbon(75887)

Question 1117442: give the equation of the circle centered at the origin and passing through the point (0,-8).
Click here to see answer by Alan3354(69443)

Question 1117443: The sum of 3 numbers in arithmetic progression is 39. If these numbers are increased by 1,5,and 12 respectively the new numbers will be in geometric progression. Find the aecond term of the geometric progression?
Click here to see answer by rothauserc(4718)

Question 1117455: (2/5)+(6/5^2)+(10/5^3)+...s.n.=?

Click here to see answer by Fombitz(32388)

Question 1117449: Sum of the series 2/5+6/5^2+10/5^3��.full process

Click here to see answer by ikleyn(52787)

Question 1117408: The value of a new car purchased for $78,000 depreciates at a rate of 15% in the first year and 4% every year after that.
a) Determine the value of the car at the end of the year, the second year and the third year. Write these values as a sequence.
b) Determine the explicit formula for the value of the end on year n.
c) What is the value of the car at the end of year 20?
Click here to see answer by josgarithmetic(39617)

Question 1117534: may you please help me, i need assistance in mechanics on the topic of forces in equilibrium and friction. the question reads:A small block of weight W newtons is placed on a plane inclined at an angle theta to the horizontal. The coefficient of friction between the block and plane is mu.
a) If mu=1/5 and tan (theta)=3/4 find, in terms of W, the magnitude of the horizontal force needed to prevent the bock from slipping down the plane.
b) If mu=2/5 and theta=60 degrees find, in terms of W, the magnitude of the horizontal force that will be on the point of making the block slide up the plane.
Click here to see answer by solver91311(24713)

Question 1117536: 0, 1, 4, 10, 20, 35�.
Click here to see answer by ikleyn(52787)

Question 1117535: 0, 1, 4, 10, 20, 35�.
Click here to see answer by ikleyn(52787)

Question 1117535: 0, 1, 4, 10, 20, 35�.
Click here to see answer by greenestamps(13200)

Question 1117596: Find (a,b)such that
(picture of equation as it was to complex to write it in text) http://tinypic.com/r/23vyphg/9

Click here to see answer by solver91311(24713)

Question 1117673: if th 10th of an AP is double the 2nd find the 8th term given that a=7
Click here to see answer by ikleyn(52787)

Question 1117673: if th 10th of an AP is double the 2nd find the 8th term given that a=7
Click here to see answer by josgarithmetic(39617)

Question 1117883: In a bacteria strain, the number of bacteria doubles every 20 minutes. There were 8 bacteria to start with. How many bacteria will there be after 3 hours?
Click here to see answer by ikleyn(52787)

Question 1118014: Determine the sum of the geometric sequence: 1 + 5 + 25 + ... + 3125.
Click here to see answer by ikleyn(52787)

Question 1118059: 14,20,26 10,24,38 44,28,12 22,?,14
Click here to see answer by math_helper(2461)

Question 1118070: Find the sum of the series 1+3.5+6+8.5+......+101
Find the sum of the first 23 term of the AP 4-3-10.....
An arithmetic series have 1st term as 4 and common difference as 1/2 find the first 20term
Find the sum of the first 100 term
Find the sum of arithmetic series term 1common difference 3 and last term 100
Find the sum of d first 20 term of arithmetic is identical to the sum of first 22 term. If the common difference is -2 find the first term
Osakpolormario@gmail.com

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