Tutors Answer Your Questions about Sequences-and-series (FREE)
Question 44039: Please help me solve the following problems. I've tried to solve the problem but I don't it correct.
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a)What is d, the difference between any 2 terms?
Answer:
d = 2
Show work in this space.
3-1=2
5-3=2
b)Using the formula for the nth term of an arithmetic sequence, what is 101st term?
Answer:
an = 1 + (n - 1)2
Show work in this space.
c)Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer:
Sum a20 = 400
Show work in this space
Sum an = n[2a1 + (n - 1)d] / 2
Sum a20 = 20[2 + (20 - 1)2] / 2
Sum a20 = 10[2 + (20 - 1)2]
Sum a20 = 10[2 + (19)2]
Sum a20 = 10[2 + 38]
Sum a20 = 10[40]
Sum a20 = 400
d)Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms?
Answer:
Sum a20 = 900
Show work in this space
Sum an = n[2a1 + (n - 1)d] / 2
Sum a20 = 30[2 + (30 - 1)2] / 2
Sum a20 = 15[2 + (30 - 1)2]
Sum a20 = 15[2 + (29)2]
Sum a20 = 15[2 + 58]
Sum a20 = 15[60]
Sum a20 = 900
e)What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."
Answer:
N an Sum
1 1
2 3 4
3 5 9
4 7 16
5 9 25
6 11 36
7 13 49
8 15 64
9 17 81
The sum of the nth in the series is the square of n.
Click here to see answer by venugopalramana(3286)  |
Question 44372: I'm having problem soving the following problems. Please help.
2) Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
Answer:
Show work in this space.
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Answer:
Show work in this space
3) Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:
Show work in this space.
b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.
Answer:
Show work in this space.
c) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms? Please round your answer to 4 decimals.
Answer:
Show work in this space.
d) What observation can make about these sums? In particular, what number does it appear that the sum will always be smaller than?
Answer:
4) CLASSIC PROBLEM - A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space
Click here to see answer by venugopalramana(3286) |
Question 44629: I've got this problem (see below). I've worked through problems 1b - 1d, but I am stuck with how to answer 1e. Can someone help?
Thanks A Bunch!
1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,…to find the following:
a) What is d, the difference between any 2 terms?
Answer: d = 2
Show work in this space.
The difference between any two terms = (n+1 ) th term - (n) th term
So, the difference d = 3-1 = 5-3 = 7-5 = 2
Answer d = 2
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term?
Answer: nth term = 201
Show work in this space.
Given a = first term = 1
n = 101
d = 2
putting above values in formula 1
nth term = 1 + (101-1) * 2
= 1 + 200 = 201
So, nth term = 201
c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms?
Answer: 400
Show work in this space
n = 20
a = first term = 1
So, sum = 20 / 2 (2 * 1 + 19 * 2)
= 10 * (40)
sum = 400
d) Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms? =n/2(a +(n-1)d)…………..(1)
Answer: 900
Show work in this space
given that n = 30
a = first term =1
= 30 / 2 (2 * 1 + 29 * 2)
=15 * (60)
= 900
e) What observation can you make about these sums of this series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Express your observations as a general formula in "n."
Answer:
Click here to see answer by stanbon(75887) |
Question 44597: A traveling salesman (selling shoes) stops at a farm in the Midwest. Before he could knock on the door, he noticed an old truck on fire. He rushed over and pulled a young lady out of the flaming truck. Farmer Brown came out and gratefully thanked the traveling salesman for saving his daughter’s life. Mr. Brown insisted on giving the man an award for his heroism.
So, the salesman said, “If you insist, I do not want much. Get your checkerboard and place one penny on the first square. Then place two pennies on the next square. Then place four pennies on the third square. Continue this until all 64 squares are covered with pennies.” As he’d been saving pennies for over 25 years, Mr. Brown did not consider this much of an award, but soon realized he made a miscalculation on the amount of money involved.
a) How much money expressed in dollars would Mr. Brown have to put on the 32nd square?
Answer:
Show work in this space
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
Answer:
Show work in this space
c) Calculate the amount of money necessary to fill the whole checkerboard (64 squares). How money expressed in dollars would the farmer need to give the salesman?
Answer:
Show work in this space
Click here to see answer by venugopalramana(3286) |
Question 44658: PLEASE, PLEASE HELP ME!!!!!!!!!!!
Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
Include the following in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric sequence?
Give at least two real-life examples of a sequences or series. One example should be arithmetic, and the second should be geometric. Explain how these examples would affect you personally.
Click here to see answer by stanbon(75887) |
Question 45922: Hi again,
This type of problem is still giving me some trouble:
The sum of the squares of two numbers is 117. The difference of the squares of the same two numbers is 45. Find the numbers.
Thanks again,
Louis
Click here to see answer by abhijitvakil(7) |
Question 46786: The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
0,2,6,12,20,...
A) a n=n^2-n
B) a n=2n-2
C) a n=4n-6
D) a n=2^n-1 -1
I have looked but am unable to understand how these patterns work. Please help!
Thanks!
Click here to see answer by Nate(3500) |
Question 46789: A pendulum bob swings through an arc 70 inches long on its first swing. Each swing, thereafter, it swings only 89% as far as on the previous swing. What is the length of the arc after 9 swings?
Round your answer to two decimal places, if necessary.
I need to know how to set this problem up please. I get mixed up when trying to set it up and then become completely frustrated! Please help!
Click here to see answer by adamchapman(301) |
Question 46993: What is the degree of the polynomial -4x(to the third power)+2x(to the second power)y-5xy(to the fourth power)
and also
which of the following is a monomial with a degree of 7
a.-2x(to the third power)y( to the second power)
b.4x(to the fourth power)+ 5xy( to the second power)
c.7x
d.x( to the fifth power) yz
Click here to see answer by mathchemprofessor(65) |
Question 47551: Can u show me how to find the sum of all the complex zeroes of f(x)=x^3-x^2-x+33
Also can u show me how to find a polynominal function of degree 5 with rational coefficient has negative 5,2 minus square root 3, and negative 5 minus 2i
Click here to see answer by stanbon(75887) |
Question 47852: I solved this problem but I need somebody to please confirm my answer is right. Thanks.
7
__
\
\ (-1/3)^n = - 547/2187
/
/__
n=0
Sn = ( -1/3)^0 + (-1/3)^1+(-1/3)^2+ (-1/3)^3 +(-1/3)^4+ (-1/3)^5 + (-1/3)^6 +
(-1/3)^7
= 0 + (-1/3) + 1/9 + (-1/27) + 1/81 + (-1/243) + 1/729 + (-1/2187)
= -547/2187
Click here to see answer by Earlsdon(6294) |
Question 48068: 8,4,4,4,1/2,1/4,1/8.....
Can you guest what the next term is(the 8th term)? Now can you make a formula which will tell you what the 100th term is?
I guess the next term is 1/16, but I don't know formula to figure out the 100th term.
Click here to see answer by Nate(3500) |
Question 48216: This is not an exact number in my book it is on a worksheet , “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.? Please show how you got your answer
Click here to see answer by stanbon(75887) |
Question 48303: I'm not too sure how to write this, but the problem is ... a four is over the sign for sigma and under it is m=1 then (2/m - 2/m+1) I am to write this sum without using sigma notation; then compute the sum. Please help if you can. Thank you!
Click here to see answer by Nate(3500) |
Question 48342: i'm not sure if this question is in the right section. its not from a textbook, it is from an algebra II honors summer packet.
it says:
name the sets of numbers to which each number belongs.
use N, W, Z, Q, I, or R.
and the numbers are:
-1/3, sqrt5, and pi.
to me it is very vague, but that is all the information i was given. maybe the letters have a specific meaning that i was never taught. any help at all would be greatly appreciated.
Click here to see answer by stanbon(75887) |
Question 48342: i'm not sure if this question is in the right section. its not from a textbook, it is from an algebra II honors summer packet.
it says:
name the sets of numbers to which each number belongs.
use N, W, Z, Q, I, or R.
and the numbers are:
-1/3, sqrt5, and pi.
to me it is very vague, but that is all the information i was given. maybe the letters have a specific meaning that i was never taught. any help at all would be greatly appreciated.
Click here to see answer by AnlytcPhil(1806)  |
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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
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