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

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 Algebra: Sequences of numbers, series and how to sum them Solvers Lessons Answers archive Quiz In Depth

 Question 52669: Solve the system using the substituion method. 2x - 5y = 9 -3x + y = -7 Click here to see answer by AnlytcPhil(1276)

 Question 52643: 2) For the function y = x2 - 4x - 5, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. Answer: Show work in this space b) What is the equation for the line of symmetry for the graph of this function? Answer: c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x – h)2 + k. Show graph here. Explanation of graphing. d) In your own words, describe how this graph compares to the graph of y = x2? Answer: Click here to see answer by venugopalramana(3286)

 Question 53287: 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. Click here to see answer by Nate(3500)

 Question 53517: 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 series, 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 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.)? Express your observations as a general formula in "n." Answer: I think I got it but i'm not sure. Click here to see answer by venugopalramana(3286)

 Question 53538: 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 series, 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 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.)? Express your observations as a general formula in "n." Answer: Click here to see answer by funmath(2925)

 Question 25541: I have an assignment due on arithmetic series of numbers. I have been studying my book and can't seem to figure out what I am supposed to do to make or solve the equations. Is there anyway you can help? Thank you in advance. Use the arithmetic series of numbers 1,3,5,7,9,...to find the following: What is d, the difference between any 2 numbers? Using the formula for the nth term of an arithmetic series, what is 101st term? Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? Using the formula for the sum of an arithmetic series, what is the sum of the first 30 terms? 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.)? I know it seems like a lot but it really is just one problem broken down into several sections. I have no idea how to so this so I would be VERY thankful for any help you can give me. Click here to see answer by vanetiks(6)

 Question 53618: I am totally lost, Please help!!! 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 a sequences or series. One example should be arithmetic, and the second should be geometric. Click here to see answer by stanbon(57219)

 Question 53621: I am having a hard time figuring out this problem. 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. Thanks for your help! Click here to see answer by stanbon(57219)
 Question 53621: I am having a hard time figuring out this problem. 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. Thanks for your help! Click here to see answer by funmath(2925)

 Question 53667: Use the arithmetic sequence of numbers 1. 3, 5, 7, 9,...to find the following: a) what is d, the differenc between any 2 terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101th term? c) Using the formula for the sum of an arthmetic series, what is the sum of the first 20 terms? Click here to see answer by stanbon(57219)

 Question 43662: Using the data set 17, 25, 30, 27, 16, 19, 35, 42, 18, 20, 19, 13, what value corresponds to the 43rd percentile? a) 17 b) 19 c) 21 d) 23 e) NOT Click here to see answer by stanbon(57219)

 Question 53970: OK so say you had a quadratic sequence that represented pascales triangle so the first row would be 1 cube and the second row would be 4 cubes the third row would be 9 cubes and so on there for the sequence being 1,4,9,16,25.... there for the eqasion would be tn= n^2. Then you would want to find the 100th row which would be 100^2 but the question is how many blocks would it take to build up to the 100th row so its the sum of the sequence or pyrimd up to t100. Now you could just add up all the terms in the sequence but i would like to know the equaion for finding the sum of this term, and how you would get that equasion. If you could e-mail me ASAP that wouls be greatly appreciated thanks for the help FELICIA Click here to see answer by stanbon(57219)

 Question 54068: 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) Whcih 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 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(57219)

 Question 54071: Consider the arithmetic sequence; 2,7,12,17,22,.... what is the ordinal of the term 102? Click here to see answer by stanbon(57219)

 Question 54265: 3, 6, 11, 18 ... The first four terms of a sequence are shown above. Which of the following could be the formula that gives the nth term of this sequence for all positive integers n? A. 2n B. 2n + 1 C. 3n D. n^2 + 1 E. n^2 + 2 Click here to see answer by Nate(3500)

 Question 54481: if 5x - x = 2x + x - 5 then x = Click here to see answer by tutorcecilia(2152)

 Question 54684: the nth term in an arithmetic sequence is represented by tn. If tp=p squared and tq=q squared find the common difference. Click here to see answer by psbhowmick(529)

 Question 54872: Hello, I couldd really use some help on this one. Thanks! Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. How much time did each require? Click here to see answer by ankor@dixie-net.com(15624)

 Question 54813: Hi, hope you can help me withs this problem A new car depreciates by 20% in its first year. Each succeding year it depreciates by 10%. Assume the car is still in good work condition after 10 years. If the car cost \$25000 calculate the value of the car after 10 years. Express your answer to the nearest \$10 Tanks for your help! Click here to see answer by stanbon(57219)

 Question 55340: Hi, I am having a hard time trying to resolve this problem Donna deposited some money into an account paying 8% per annum, compounded quarterly. When she goes into the bank 3 years later, she discovers that there is \$1585.30 in her account. What was the initial amount Donna deposited? Any help will be eternally appreciated thanks Click here to see answer by checkley71(8403)

 Question 55341: Hi guys, hope you can help me with this problem. I tried to figure it out by myself but I am completely lost. Here it is: Kenneth recently started a new job. His starting gross monthly salary is \$3200. Each year, on the anniversary of his starting date, Kenneth is promised a 7% raise. A.If Kenneth works for 5 years, what was his gross annual income in his fifth year at work? B.What is the minimum of years Kenneth will have to work to earn a gross annual income of at least \$60000? Thanks in advanced!!! Click here to see answer by checkley71(8403)

 Question 55465: Good evening, I have the problems about the GP and Ap. Please help me in..... 1) A ball is dropped from a height of 18 ft. If on it rebound, it rises to a height 2/3 the distance from which it fell, how far ( up and and down ) will the ball have traveled when it hits the ground for the sixth times? (Give the approximately answer) 2) A pendulum is released and swings through an arc measuring 15 inche. Each swing thererater it travels a distance 0.85 times the length of the previous pass. Approximately how far will the pendulum swing on the eighth pass? 3) A readioactive dye is injected into a system in a medical test. After one hour, 60% of the dye remains. At the end of two hours 60% of the remaining dye remains, and so on. If one unit of dye is injected, approximately what percent will remain after 12 hours? Click here to see answer by venugopalramana(3286)

 Question 55486: 1)The first two terms of a geometric sequence are a1=1/3 and a2=1/6. what is a8 the 8th term? 2)If x is inversely proportional to y and x =60 when y =0.5 find x when x=12 3)An infinite geometric series has 1 ad 1/5 as its first 2 terms: 1, 1/5, 1/25, 1/125,... what is the sum, S, of the infinite series? 4) if y=7.2 when x=10 what is the value of x when y =20? (y varies inversely as the square of x) Click here to see answer by stanbon(57219)

 Question 55720: Hello, I am having trouble figuring out this problem Write a recursive formula that generates the terms of the following: 1,3,9,27,... Thanks in advanced Click here to see answer by stanbon(57219)

 Question 56302: On the day of the child's birth, a proud parent deposits an amount of money into a compound interest savings account, which will earn 5% each year. On the child's eighteenth birthday, the account will have accumulated \$10,000. How much did the parent deposit on the day of the child's birth? Click here to see answer by stanbon(57219)

 Question 56307: Determine whether the following argument is correct. If it's not correct, explain what is wrong with the argument and change the minor premise to make a correct argument. All NBA basketball players are over 5 ft. tall. Russell is 6 ft. tall. Therefore, Russell plays in the NBA. Click here to see answer by stanbon(57219)

 Question 56303: Consider the sequence that begins 4, 3, ... and continues by the rule: Every subsequent element of the sequence is the sum of the two preceding elements. a. Determine the next five (third through seventh) elements of this sequence. b. Compute the ratio of the sixth and seventh elements of this sequence. Is it close to the Golden Ratio? Click here to see answer by Cintchr(481)

 Question 57164: here's the sequence: 1, 1/4, 1/9 ,1/16 or 1, .25, 1.111111repeating, .0625 What is the pattern?? and if you figure out the pattern, i'll find out on my own the next two numbers. Click here to see answer by funmath(2925)
 Question 57164: here's the sequence: 1, 1/4, 1/9 ,1/16 or 1, .25, 1.111111repeating, .0625 What is the pattern?? and if you figure out the pattern, i'll find out on my own the next two numbers. Click here to see answer by checkley71(8403)
 Question 57164: here's the sequence: 1, 1/4, 1/9 ,1/16 or 1, .25, 1.111111repeating, .0625 What is the pattern?? and if you figure out the pattern, i'll find out on my own the next two numbers. Click here to see answer by rcmcc(152)

 Question 57165: here's the sequence: 0.001,0.01,0.1,1 Whats the pattern?? if you figure it out i'll find the next two numbers on my own. thanks Click here to see answer by funmath(2925)
 Question 57165: here's the sequence: 0.001,0.01,0.1,1 Whats the pattern?? if you figure it out i'll find the next two numbers on my own. thanks Click here to see answer by checkley71(8403)

 Question 57171: here's the sequence: 12, -4, 4/3, -4/9 what is the next two numbers??(or give me the pattern and i'll figure them out) thanks Click here to see answer by checkley71(8403)

 Question 57176: what is the function rule if: x f(x) -1 1 -2 8 -3 27 -4 64 Click here to see answer by stanbon(57219)

 Question 57214: Sum this series of numbers: 1+4+7+10+13+16+....+8938+8941+8944. How do you find the number of integers and how do you solve? I got 1491 integers [1+(n-1)*3 = 8944 and Sum [n/2*(1+8944)]= 13,336,995. Click here to see answer by stanbon(57219)

 Question 57246: What is the rule for this pattern? 1,3,5,6,5,15,14,42 i think it is (nX3)-1 Math 4 Today Test #18 Click here to see answer by Scriptor(36)

 Question 57346: Hello, Could you help me on the solution to this question, The sum of a series is given by the formula Sn=(4^n)(n-3). Determine the value of the 6th term. Thanks all!. Click here to see answer by stanbon(57219)

 Question 57601: could you show me how to write the series 1+(1/2)+(1/4)........(1/4096) in sigma notation. I havent done this in some time. Regards. Len. Click here to see answer by stanbon(57219)

 Question 59091: 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. You can this r easily by taking the ratios 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 series, what is the sum of the first 10 terms? Answer: Show work in this space. Click here to see answer by funmath(2925)

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