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 84140: 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: r=1/2 divided by 1,
which is 1/2(fraction)
Is this correct
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? Round your answer to 4 decimals.
show work
1st term is 1X1/2=1/2
2nd term is 1/2X1/2=1/4
3rd term is 1/4X1/2=1/8
4th term is 1/8X1/2=1/16
5th term is 1/16X1/2=1/32
6th term is 1/32X1/2=1/64
7th term is 1/64X1/2=1/128
8th term is 1/128X1/2=1/256
9th term is 1/256X1/2=1/512
10th term is 1/512X1/2=1,024
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? Round to 4 decimals.
show work
11th term is 1/1,024X1/2=2,048
12 term is 1/2,048X1/2=4,096
d) What observation can you make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?
1
Click here to see answer by jim_thompson5910(35256)

Question 84141: 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
16,384

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
16,384

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
20,096

Click here to see answer by jim_thompson5910(35256)

Question 84183: Can anyone help me Im not sure if I even have what I have right
Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,�to find the following:
a) What is d, the difference between any two consecutive terms?
Answer: 2
Show work in this space.
1(3-5) =2
1(7-9) =2
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: 10,050.5
Show work in this space.
a =50.5+ (101-1) (-100)=50.5+100(-100)=10,050.5

c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
Answer:
Show work in this space

d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
Answer:
Show work in this space

e) What observation can you make about these sums of this sequence (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 jim_thompson5910(35256)

Question 84239: Hello I really need help. PLEASE HELP ME...

Use the geometric sequence of numbers 1, 3, 9, 27, � to find the following:
a) What is r, the ratio between 2 consecutive terms?
Show work in this space.

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Show work in this space.

c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?
Show work in this space.

Click here to see answer by vertciel(183)

Question 84832: Please, assist me in this math problem. THANKS!
Find fractional notation for each infinite sum.
0.454545...
and
1.36666...
Click here to see answer by Earlsdon(6294)

Question 84831: Determine whether the following goemetric series has a FINITE sum. If a finite sum exists, find it.
1. 8+4+2+....
2. 2+3+9/2+....
Thanks!
Click here to see answer by jim_thompson5910(35256)

Question 84876: I tried this problem but still can't figure it out after hours of calculations.
What number comes next in the sequence??
61, 691, 163, 487, 4201, ___ ?
Thank you so much for helping.

Click here to see answer by jim_thompson5910(35256)

Question 84882: Please help me to figure out this word problem. Thank you.
Suppose an employee recieves a wage of 1 cent for the first day of work, 2 cents the second day, 4 cents the third day, and so on in a geometric sequence. Find the total amount of money earned for working 30 days.
Click here to see answer by Earlsdon(6294)

Question 84906: Does anyone have any insight into the type of problem below? If so, can you help me? I don't know what I'm doing.

PROBLEM - A traveling salesman 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 Crane came out and gratefully thanked the traveling salesman for saving his daughter�s life. Mr. Crane 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 grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat.� As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
a) How much wheat would Mr. Crane have to put on the 24th square?
Answer:

Show work here please:

b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Answer:
Show work please:

c) Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
Answer:

Click here to see answer by jim_thompson5910(35256)

Question 85266: how many integers between 299 and 501 are divisible by 2 or 5
Click here to see answer by scianci(186)

Question 85811: A census taker asked Ms. Steman the ages of her three sons. She said, "The product of their ages is 36. The sum of their ages is equal to the number of the house next door." The census taker walks next door, looks at the house number and returns to say, "You haven't given me enough information." Ms. Steman then said, "My oldest son is sleeping upstairs." How old are Ms. Steman's sons? - WHAT FORMULA OR PROCESS DO I USE IN ORDER TO DETERMINE AN ANSWER??
Click here to see answer by scianci(186)

Question 85822: This should be an easy question, I'm just stumped.
Write down the nth term of the sequence suggested by the pattern 1, 1/2, 3, 1/4, 5, 1/6, 7, 1/8,...
Any help would be nice.
Click here to see answer by bucky(2189)

Question 85983: please,sir,help me urgently solve this question.
the question is- 1cube = 1square
1cube + 2cube + 3cube= 9+27 = 36 =(1+2+3)whole square
1cube + 2cube + 3cube + 4cube= 36+64=100=(1+2+3+4)whole square
use this pattern to find the sum of the cubes of the first ten natural numbers.
Click here to see answer by 303795(602)

Question 86092: If the sequence above continues in the same pattern, how many
small triangles would be needed to make the figure that would
occur in Step 5?
Click here to see answer by jim_thompson5910(35256)

Question 86182: here is another problem i seriously can't work out:
X 1,2,3,4,5
Y 5,8,11,14,17
what is the rule to find the numver of y's if x=30
my answer was y=1x-27 but i doubt this is right
Click here to see answer by psbhowmick(878)

Question 86181: i am having trouble with my algebra homework and trying to work out if it is right.Here's my question:
X 1,2,3,4,5
Y 5,8,11,14,17
use the table above to write the rule that tells you how many of y you can get for any number of x's.
The way i worked it out is by finding out the first difference which is 3 so then i said add 2 to make it 5 so this was my answer: 3x+2
I was wondering if i was correct and if i was wrong could you please tell me a way to work it out.
Click here to see answer by stanbon(75887)

Question 87087: 1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10� to find the following:
a) What is d, the difference between any two consecutive terms?
Answer:
Show work in this space.

b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:
Show work in this space.

c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
Answer:
Show work in this space.
Click here to see answer by jim_thompson5910(35256)

Question 87108: This is a long one I know, can someone please help me with this one?
Use the arithmetic sequence of numbers 2, 4, 6, 8, 10� to find the following:
a) What is d, the difference between any two consecutive terms?
Answer:

b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer:

c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
Answer:

d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
Answer:

e) What observation can you make about the successive partial sums of this sequence (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)?

Click here to see answer by jim_thompson5910(35256)

Question 87110: Any help here?
Use the geometric sequence of numbers 1, 3, 9, 27, � to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer:
C) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?
Answer:

3) Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27� to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:

Click here to see answer by jim_thompson5910(35256)

Question 87109: Can you solve this one? : )
Use the geometric sequence of numbers 1, 1/3, 1/9 , 1/27� to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer:

b) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer:

c) Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
Answer:

d) What observation can make about the successive partial sums of this sequence? In particular, what number does it appear that the sum will always be smaller than?

Click here to see answer by jim_thompson5910(35256)

Question 87164: Use the geometric sequence of numbers 1, 3, 9, 27 � to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer: r =3
Show work in this space.
1*3=3 3*3=9 3*9=27 ECT�

b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
Answer:
Show work in this space.

Use the geometric sequence of numbers 1, 1/3, 1/9, 1/27� 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 sequence, what is the sum of the first 10 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.

c)Using the formula for the sum of the first n terms of a geometric sequence, what is the sum of the first 12 terms? Carry all calculations to 6 decimals on all assignments.
Answer:
Show work in this space.

d) What observation can make about the successive partial sums of this sequence? In particular, what number does it appear that the sum will always be smaller than?
Answer:
I really need help on these problems. I am at a total lose here. Please Help me out. Thank you!

Click here to see answer by jim_thompson5910(35256)

Question 87197: 2) Use the geometric sequence of numbers 1, 3, 9, 27, � 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 10th term?
Answer:
Show work in this space.

c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?
Answer:
Show work in this space.
Click here to see answer by jim_thompson5910(35256)

Question 87237: Use the geometric sequence of numbers 1, 3, 9, 27, � 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 10th term?
Answer:
Show work in this space.

c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?
Answer:
Show work in this space.

Click here to see answer by jim_thompson5910(35256)

Question 87251: I would really appreciate any help with this problem. If i learn this one i should be able to do the others following. Write a recursive rule for the sequence. The sequence may be arithmetic, geometric, or neither. 6,10,14,18,22..
Click here to see answer by longjonsilver(2297)

Question 87314: Find the number of terms and the sum of the series 7+17+27+...+107
Click here to see answer by jim_thompson5910(35256)

Question 87308: Trying to help my daughter with her homework... It's been way too long since I did this! Thanks for any help!
Write the following series using sigma notation:
1+2+3+4+5+...98+99+100
Click here to see answer by scott8148(6628)

Question 87426: Find the sum of the first 10 terms of the series 6.4, 3.2, 1.6, ...
Click here to see answer by stanbon(75887)

Question 87502:
Click here to see answer by rapaljer(4671)

Question 87531:
Click here to see answer by rapaljer(4671)

Question 87532: which one of the basic functions (liner, quadratic, rational, or exponential) is related to the arithmetic series?
Click here to see answer by Nate(3500)

Question 88424: could you give me some REAL LIFE examples of arithmetic progressions please??(at-least TWO examples)?
Click here to see answer by stanbon(75887)

Question 88447: What is the sum of the first 50 natural numbers?
Click here to see answer by stanbon(75887)

Question 88447: What is the sum of the first 50 natural numbers?
Click here to see answer by checkley75(3666)

Question 88472: What is the sum of the first 15 terms in the geometric sequence 2, 4, 8?
sometimes i got 65534 and sometimes i got 65536, im doing something wrong lol
Click here to see answer by bucky(2189)

Question 88544: find the value of a[3] if: n=3 and a[n] =2n-3/n
i dont know why the n-th numbers are not comming out right, but i think the answer is 6 can someone help with this, thanks!
Click here to see answer by stanbon(75887)

Question 88545: if a[1]=4 and d=-2, what are the first four terms of the arithmetic sequence?
Click here to see answer by stanbon(75887)

Question 88693: if a[1]=4 and r=2, what are the first four terms of the geometric sequence? I think its 4, 6, 8, 10 but im not positive
Click here to see answer by Earlsdon(6294)

Question 88820:
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 88818:
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89745: Solve the problem.
The Family Fine Arts Center charges $21 per adult and $13 per senior citizen for its performances. On a recent weekend evening when 535 people paid admission, the total receipts were $8355. How many who paid were senior citizens?
I am struggling with the right formula to use. Do I use an arthimetic or geometric sequence? Thanks in advance for the help! Annie C.
Click here to see answer by ankor@dixie-net.com(22740)

Question 89891: Short answer. Write the word or phrase that best completes each statement or answers the question.
Find the value of k if you have the matrix:
5,9
-2,k = 8
I can't seem to even get going on this one. Not sure what to do.
Thanks,
Annie C.
Click here to see answer by stanbon(75887)

Question 89889: I am just not getting this section....
Use the formula for S[n] to find the sum for the geometric sequence: 4,-16,64,-256,1024.
Thanks in advance.
Annie C.
Click here to see answer by stanbon(75887)

Question 89892: Use mathematical induction to prove the statement is true fro all positive integers, n:
6+12+18+....6n=3n(n+1)
Do I just divide this out? I.e. 12/6=2....?
Click here to see answer by mathmaven53(29)

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