# Questions on Algebra: Sequences of numbers, series and how to sum them answered by real tutors!

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 Question 36866: I have tried to do the problem "For each arithmetic series, find S of 25" 3+7+11+15 This is the equation i came up with 25[2(3)+(25-1)d/2] I just cant find the d and when i try my answer comes out incorrect.. thanks.. Click here to see answer by stanbon(60771)

 Question 36923: For the sequence below how would you solve this: write a recursive formula and fine the next three terms? 3,9,15,21 Click here to see answer by Alwayscheerful(414)

 Question 36901: "Write the first four terms of the geometric sequence with the first term (a sub n = 16) and common ration r= -1/2. Click here to see answer by venugopalramana(3286)

 Question 37242: What is the next number in this sequence and how do you get it? 1,2,5,10,4,8,20,40,? Thank You Click here to see answer by checkley71(8403)
 Question 37242: What is the next number in this sequence and how do you get it? 1,2,5,10,4,8,20,40,? Thank You Click here to see answer by AnlytcPhil(1321)

 Question 37581: Find aV8 if aV1 =-21, aVn=aVn-1^-3; for n=2,3,4,... I have no idea how to do any of these problems! This is going to be so very hard. Click here to see answer by venugopalramana(3286)

 Question 37577: Write the first four terms of the sequence an=64(1/4)^n, for n=0, 1, 2, 3, How do I finish problem? Click here to see answer by venugopalramana(3286)

 Question 37688: Evaluate 70!/68!. How do I do this problem? Thank you. Click here to see answer by Alwayscheerful(414)

 Question 37829: In an arithmetic sequence, a1=23 and a8=44. Find the fifth term a5. I have no idea how to do these problems. Please show me the steps to solve this problem. Thank you. I am getting 35 for an answer and don't think that I am right. Click here to see answer by longjonsilver(2297)

 Question 37826: Write 0.8(with a line over the 8) as a fraction in lowest terms. How do I do this? Thank you. Click here to see answer by longjonsilver(2297)

 Question 37825: Determine which of the following can be the first three terms of an geometric sequence. a. 3,-3,-3 b. -8,-16,-32 c. 26,30,34 d. 1/2,1/4,1/16 please help me solve this problem. Thank you. Click here to see answer by fractalier(2101)

 Question 37824: Determine which of the following can be the first three terms of an Arithmetic sequence. a. 1/2,1/4,1/8 b. -8,-16,-32 c. -42,-37,-32 d. 4,-1,6 I have no idea which one it is. Could you please help me? Thank you. Click here to see answer by fractalier(2101)

 Question 37792: A tank contains gallons of water. Each day one-third of the water in the tank is removed and not replaced. How much water remains in the tank at the end of 6 days? i tried doing this a few times and im not getting the right answer. I think you write it like this: a=5832(1/3)^(6-1) right? Click here to see answer by fractalier(2101)

 Question 37943: Evaluate -8 / -4 A) -4 B) -2 C) 2 D) 4 Click here to see answer by checkley71(8403)

 Question 37974: find f(x) -g(x) when f(x) is x-1 and g(x) is 2x squared. Click here to see answer by fractalier(2101)

 Question 37948: Solve for X: 5(X + 2) – 7 (2X – 3) = 22 A) -1 B) -3/2 C) 3/2 D) 1 Click here to see answer by checkley71(8403)

 Question 37929: Which number is prime? A) 1 B) 8 C) 42 D) 61 Click here to see answer by fractalier(2101)

 Question 37941: Evaluate | 6 | - | -2 | A) 4 B) -4 C) 8 D) -8 Click here to see answer by fractalier(2101)

 Question 38029: write the first four terms of the sequence a1=-3, an=(-2)an-1;n=2,3,4,... How do I do this problem? Is the answer -3,-5,-7,-9 or did I do it wrong? Thank you. Click here to see answer by stanbon(60771)

 Question 38034: Two cards are dealt from a well-shuffled deck of 52 cards. What is the probability that both cards are aces, given that the first card is an ace? Help! Click here to see answer by stanbon(60771)

 Question 38033: The executive committee of the student government consists of 10 members. In how many ways can a chair, vice-chair, secretary, and a treasure be chosen, assuming one person cannot hold more than one position? Please help! Click here to see answer by stanbon(60771)

 Question 38187: Calculate the sum of all even positive integers from 2 to 4000. Click here to see answer by fractalier(2101)

 Question 38571: Compare the values in Column A and Column B for the solution of the system: { x + y + z = 10 x + y + 2z = 13 x + y + 3z = 16 Column A = x Column B = y A The value in Column A is greater B The value in Column B is greater C The two values are equal D The relationship cannot be determined on the basis of the information supplied I'm just not sure!!! Thanks!! Click here to see answer by AnlytcPhil(1321)

 Question 38761: 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: 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? Carry all calculations to 7 significant figures. 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? Carry all calculations to 7 significant figures. 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: Click here to see answer by Nate(3500)

 Question 38763: find the sum of he first 20 terms of the airthmetic series -2+1+4+7 Click here to see answer by Nate(3500)

 Question 39011: Don't know how to do these. Please help. 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: 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? Carry all calculations to 7 significant figures. 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? Carry all calculations to 7 significant figures. 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: Click here to see answer by stanbon(60771)

 Question 38658: write in expanded form? what does that mean? Click here to see answer by fractalier(2101)

 Question 39196: This is my last question, Thanks for all your help everybody. 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. Brown have to put on the 24nd 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 stanbon(60771)

 Question 39195: Still do not understand. Please help again. 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: 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? Carry all calculations to 7 significant figures. 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? Carry all calculations to 7 significant figures. 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: Click here to see answer by stanbon(60771)

 Question 39191: Still need help. PLease if anyone can help, it would be very appreciated. Thank you. 1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… 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 series, what is the sum of the first 20 terms? Answer: Show work in this space. Click here to see answer by kathysmiles77777(4)

 Question 39190: Still need help. PLease if anyone can help, it would be very appreciated. Thank you. 1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… 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 series, what is the sum of the first 20 terms? Answer: Show work in this space. Click here to see answer by kathysmiles77777(4)

 Question 39248: did I do this right: 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. each are multiples of 3 1*3=3, 3*3=9, 9*3=27 and so on b) Using the formula for the nth term of a geometric sequence, what is the 10th term? Answer:n=19683 Show work in this space. a(n)=a(1)(r^n-1) a(n)=1(1)*(3^10-1 a(n)=3^9=19683 c) Using the formula for the sum of a geometric series, what is the sum of the first 10 terms? Answer: s=29524 Show work in this space. s(n)= a(1)(1-r^n)/1-r s(n)= 1(1)*(1-3^10)/(1-3)=29524 Click here to see answer by fractalier(2101)

 Question 39346: I asked this question before, but I did not get all the parts to the uestion posted for some reason. So please help. This includes all the parts, plus some of the answers if my answers are correct. Thanks a bunch. 1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10… to find the following: a) What is d, the difference between any 2 terms? Answer: d=4 Show work in this space. work below The value of the 20th term, i.e., when n=20, is found by using the general term: for a=3, d=4, and n=20, its value is 3+(20−1)4=79 b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. B.sequences To find the value of the nth term in an arithmetic sequence, use the following equation: an = a1 + (n–1)d a is the standard variable used to represent a term in a sequence and n counts the term number, so an represents the term in the sequence that you’re trying to find. d is the constant. To solve the problem, just substitute 101 for n, –3 for a1, and 5 for d. a101 = -3 + (101 – 1)5 a101 = 497 part B c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? Answer: The sum of the first 29 terms would be 79 Show work in this space. work above. d) Using the formula for the sum of an arithmetic series, 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 series (HINT: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, etc.)? Answer: Click here to see answer by longjonsilver(2297)