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 83790: Can you please assist me with the following problem?
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?
b) How much money expressed in dollars would the traveling salesman receive in total if the checkerboard only had 32 squares?
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?
Thank you for your help...
Click here to see answer by jim_thompson5910(28595)

Question 83789: Can someone assist me with the following problem please?
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?
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
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.
d) What observation can make about these sums? In particular, what whole number does it appear that the sum will always be smaller than?
Thank you for your assistance...
Click here to see answer by jim_thompson5910(28595)

Question 83788: Please can you help me with the following problem.
Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
b) Using the formula for the nth term of a geometric sequence, what is the 24th term?
c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Thank you for your help.

Click here to see answer by Nate(3500)

Question 83820: Use the geometric sequence of numbers 1, 2, 4, 8,… to find the following:
What is r, the ratio between 2 consecutive terms?
Show work:
Using the formula for the nth term of a geometric sequence, what is the 24th term?
Show work:
Using the formula for the sum of a geometric series, what is the sum of the first 10 terms?
Show work:

Click here to see answer by jim_thompson5910(28595)

Question 83826: I am so confused? Please explain this to me. Thank you so much for all your help!
Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?

Click here to see answer by jim_thompson5910(28595)

Question 83819: I've tried numerous times to get this right, but I can't figure it out.
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 jim_thompson5910(28595)

Question 83722: 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:
1. Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
2. Which one of the basic functions (linear, quadratic, rational, or exponential)is related to the geometric sequence?
3. Give at least two real-life examples of sequences or series. One example should be arithmetic, and the second should be geometic. Explain how these examples would affect you personally. The one thing I can think of is age, but I don't know how to put it correctly.
Click here to see answer by jim_thompson5910(28595)

Question 83870: identify the common difference,d
2,4,6,8,10,...
Click here to see answer by stanbon(57342)

Question 83906: 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 jim_thompson5910(28595)

Question 83908: Use the geometric sequence of numbers 1, 2, 4, 8,…to find the following:
What is r, the ratio between 2 consecutive terms?

Click here to see answer by jim_thompson5910(28595)

Question 83907: 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?

Click here to see answer by jim_thompson5910(28595)

Question 83909: the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
What is r, the ratio between 2 consecutive terms?

Click here to see answer by jim_thompson5910(28595)

Question 83913: Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 12 terms?
Click here to see answer by Nate(3500)

Question 83996: Is this correct?
Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
What is r, the ratio between 2 consecutive terms?
Answer: r = (1/2)/1 = 1/2
Show work in this space.
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.
S(n) = a(1)[r ^(n + 1) – 1)/(r – 1)
S(10) = 1[(1/2) ^ 9 – 1] / [(1/2)-1]
S(10) = [-0.998046875…] / [-0.5] = 1.99609375…
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.
S(n) = a(1)[r ^(n + 1) – 1)/(r – 1)
S(12) = 1[(1/2) ^ 9 – 1] / [(1/2)-1]
S(12) = [-0.998046875…] / [-0.5] = 1.99609375…
n = 12

Click here to see answer by jim_thompson5910(28595)

Question 84018: Can someone assist me with the following problem please?
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?
b) Using the formula for the nth term of an arithmetic sequence, what is 101st term?
c) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
d) Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
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."
Thanks so much for your help.
Click here to see answer by jim_thompson5910(28595)

Question 84077: 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.
Click here to see answer by stanbon(57342)

Question 84125: 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:

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

Click here to see answer by jim_thompson5910(28595)

Question 84127: 1. Use the arithmetic sequence of numbers 1,3,5,7,9,....to find the following:
a. What is d, the difference between two consecutive terms?
show your work
**I am not sure what the teacher is asking here, but I think the answer is 1. 1+2=3+1=4+1=5 and so forth.
b. Using the formula for the n(th)term of an arithmetic sequence, what is the 101(st) term?
show your work
**Sn=n/2(a1+an) **I got 10,150.50

c.Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
show your work
**I got 400***

d.Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
show work
***I got 939***
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"
**I think the answer here is that the sequence of numbers goes up by one.
***Can you please help me, I want to make sure these answers are correct before I submit them.
Thank you so much for your time, I really appreciate it,
Jennifer
Click here to see answer by jim_thompson5910(28595)

Question 84124: 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

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 jim_thompson5910(28595)

Question 84120: 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 whole number does it appear that the sum will always be smaller than?
Answer:

Click here to see answer by jim_thompson5910(28595)

Question 84134: 1. Use the geometric sequence of numbers 1,2,4,8,...to find the following:
a. What is r, the ratio between 2 consecutive terms?
show work
***r=2/1=2

b. Using the formula for the nth term of a geometric sequence, what is the 24th term?
show work
***a n below=a, r 2-1 above
answer 615

c. Using the formula for the sum of a geometic series, what is the sum of the first 10 terms?
show work
****1,023.00****
Thank you for your help

Click here to see answer by stanbon(57342)

Question 84100: Find the pattern and predict the next term in the sequence? F,S,S,M,T
Click here to see answer by Edwin McCravy(8909)

Question 84139: Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function?
include in your answer:
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
Which 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 would effect you personally.
Click here to see answer by jim_thompson5910(28595)

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(28595)

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(28595)

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(28595)

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(6287)

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(28595)

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(28595)

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(6287)

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(28595)

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(595)

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(28595)

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(529)

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(57342)

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(28595)

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(28595)

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(28595)

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(28595)

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