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 73939: Using the formula for the sum of an arithmetic sequence, what is the sum of the first 20 terms?
Click here to see answer by psbhowmick(529)

Question 74006: 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(28598)

Question 74035: 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 LBocian(1)

Question 74008: 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:
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

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 stanbon(57387)

Question 74135: The other one didnt help

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 stanbon(57387)

Question 74005: 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 funmath(2925)

Question 73940: Using the formula for the sum of an arithmetic sequence, what is the sum of the first 30 terms?
Click here to see answer by funmath(2925)

Question 74127: x+5/x-5+3/x+5
Click here to see answer by bucky(2189)

Question 51029: Find the arithmetic mean of each pair of numbers
-square root of 2 , 3 times the square root of 2
Click here to see answer by jim_thompson5910(28598)

Question 74370: 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

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(28598)

Question 74369: 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:
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

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(28598)

Question 74429: how could I find general term in sequence not for (arthematic or geometric only) thank you
Click here to see answer by jim_thompson5910(28598)

Question 74491: 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(28598)

Question 74490: 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 whole number does it appear that the sum will always be smaller than?
Answer:

Click here to see answer by jim_thompson5910(28598)

Question 75679: Hi.
Can you please help me put
1-2+3-4+5-...
in summation notation form
Click here to see answer by stanbon(57387)

Question 75801: each stroke of a vacuum pump removes one third of the air ramianing in a container. wut percent of the original quanity of the air ramains in the container after 10 strokes, to the nearest percentage?
we r workin with geometric sequence
Click here to see answer by checkley75(3666)

Question 76063: What is the missing number in the sequence? 1/8,1/4,?,5/8... Cant see to find the number
Click here to see answer by checkley75(3666)

Question 76070: What is the missing number in the sequence? 1/8, 1/4, 3/8, ?, 5/8
did i get the right answer is it 1/2
Click here to see answer by checkley75(3666)

Question 77056: z(5)=9,z(6)=12,z(7)=15,z(8)=18. If z = lny, find a formula for y in terms of x
Click here to see answer by Edwin McCravy(8909)

Question 77148: Question The value of the nth term in a sequence is given by
the expression -5n + 2. What does the start of the sequence look like?
Click here to see answer by stanbon(57387)

Question 77147: Question The value of the nth term in a sequence is given by
the expression -5n + 2. What does the start of the sequence look like?
Click here to see answer by stanbon(57387)

Question 77470: How do you find the sum of the sequences on a problem like this - 1,2,3,4,5,6,7,8,9 ...... 60 ?
Click here to see answer by aaaaaaaa(138)

Question 77521: Help me please!
Write the explicit for the sequence:
2,5,10,17,26
thank you
Click here to see answer by 303795(595)

Question 77523: Can someone please help me with this problem?
Find a1 in a geometric series for which Sn=189, r=1/2, and an=3.
Click here to see answer by Edwin McCravy(8909)

Question 77731: I have a problem with a geometric sequence, these are all the numbers up to 10. 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. I need to find out how u get those numbers, I need to find out the equation to get it. please help me!
Click here to see answer by Earlsdon(6287)

Question 77692: I need some help with this question- I missed the unit lesson and I am having trouble getting the answer.
Given that in an arithmetic sequence t3=-2 and t7=-5, what is the formula for the nth term tn? what is the value of t11
Thanks so much
Click here to see answer by scott8148(6628)

Question 77796: Please help me!
I need to find the 10th term of the geometric sequence.
a9 = 8; r = .5
thanks
Click here to see answer by jim_thompson5910(28598)

Question 78165: the sum of 3 consecutive integrals numbers is 117. find the numbers
Click here to see answer by bucky(2189)

Question 78164: The sum of 2 consecutive odd integers is 92. find the numbers.
Click here to see answer by bucky(2189)

Question 78408: I need help with a story problem.
A diamond is purchased for $2500. Suppose it increases 5% in value each year. Find the value after 8 years.

Thanks.
Click here to see answer by stanbon(57387)

Question 78348: Use the geometric sequence of numbers 1, 3, 9, 27, … 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 10th term?
c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?

Click here to see answer by rmromero(383)

Question 78463: Last year a manufacturer had a sales total for january that was 50 percent greater than the average of the monthly sales totals for February through December. The sales totals for january was what fraction of the sales total for the year?
Click here to see answer by stanbon(57387)

Question 78519: 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?
b) Using the formula for the nth term of a geometric sequence, what is the 10th term?
c) Using the formula for the sum of a geometric sequence, what is the sum of the first 10 terms?

Click here to see answer by stanbon(57387)

Question 78546: 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(28598)

Question 78547: 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 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 in this space.

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

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(28598)

Question 78645: 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 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?
b) How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
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.

Click here to see answer by jim_thompson5910(28598)

Question 78942: 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?
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.
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.
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(28598)

Question 79225: A quiz has 8 questions with answer options A and B for each. What is the probability that by pure guess work a student answer at least 6 correctly?
Click here to see answer by stanbon(57387)

Question 79360: Question 1: find the next three terms of each sequence.
a); 2, -4, 8, -16 _______, ______, _______

Question 2: the first terim in a sequence and the pattern are given. Write the next four terms of each sequence.
a): 4x - 24; add 2 _____________ ____________ _________ _________
b): 7r+5; subtract r+2 ____________ ___________ ____________ __________
c): 2a; multiple by 3a ___________ ___________ ____________ _________

Thank you for yor help in the above question (pattern and sequences).
bj

Click here to see answer by chitra(359)

Question 79546: i need to find the sum of the first nth terms of the arithmetric series.
3+8+13+18+23
n=20
Sn=366
Click here to see answer by stanbon(57387)

Question 79738: triangular numbers are created by adding consecutive counting numbers? True or False?
Click here to see answer by Edwin McCravy(8909)

Question 79736: 1,1,2,3,5,8 That sequence is called?
Click here to see answer by sprolden(40)

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