9.2 Arithmetic Sequences And Partial Sums
333202 0902.qxd12/5/0511:29 AMPage 653Section 9.29.2Arithmetic Sequences and Partial Sums653Arithmetic Sequences and Partial SumsWhat you should learn Recognize, write, and findthe nth terms of arithmeticsequences. Find nth partial sums ofarithmetic sequences. Use arithmetic sequences tomodel and solve real-lifeproblems.Why you should learn itArithmetic sequences havepractical real-life applications.For instance, in Exercise 83on page 660, an arithmeticsequence is used to model theseating capacity of an auditorium.Arithmetic SequencesA sequence whose consecutive terms have a common difference is called anarithmetic sequence.Definition of Arithmetic SequenceA sequence is arithmetic if the differences between consecutive terms arethe same. So, the sequencea1, a2, a3, a4, . . . , an, . . .is arithmetic if there is a number d such thata2 a1 a3 a2 a4 a 3 . . . d.The number d is the common difference of the arithmetic sequence.Example 1Examples of Arithmetic Sequencesa. The sequence whose nth term is 4n 3 is arithmetic. For this sequence, thecommon difference between consecutive terms is 4.7, 11, 15, 19, . . . , 4n 3, . . .Begin with n 1.11 7 4b. The sequence whose nth term is 7 5n is arithmetic. For this sequence, thecommon difference between consecutive terms is 5. mediacolor’s Alamy2, 3, 8, 13, . . . , 7 5n, . . .Begin with n 1. 3 2 51c. The sequence whose nth term is 4 n 3 is arithmetic. For this sequence, the1common difference between consecutive terms is 4.5 3 7n 31, , , , . . . ,,. . .4 2 4454Begin with n 1. 1 14Now try Exercise 1.The sequence 1, 4, 9, 16, . . . , whose nth term is n2, is not arithmetic. Thedifference between the first two terms isa2 a1 4 1 3but the difference between the second and third terms isa3 a2 9 4 5.
333202 0902.qxd12/5/0565411:29 AMChapter 9Page 654Sequences, Series, and ProbabilityIn Example 1, notice that each of the arithmetic sequences has an nth termthat is of the form dn c, where the common difference of the sequence is d. Anarithmetic sequence may be thought of as a linear function whose domain is theset of natural numbers.anThe nth Term of an Arithmetic Sequencea n dn cThe nth term of an arithmetic sequence has the forman dn cca1FIGUREa2a3Linear formwhere d is the common difference between consecutive terms of thesequence and c a1 d. A graphical representation of this definition isshown in Figure 9.3. Substituting a1 d for c in an dn c yields analternative recursion form for the nth term of an arithmetic sequence.n9.3an a1 n 1 dExample 2The alternative recursion formof the nth term of an arithmeticsequence can be derived fromthe pattern below.a1 a11st terma2 a1 d2nd terma3 a1 2d3rd terma4 a1 3d4th terma5 a1 4d5th termFinding the nth Term of an Arithmetic SequenceFind a formula for the nth term of the arithmetic sequence whose commondifference is 3 and whose first term is 2.SolutionBecause the sequence is arithmetic, you know that the formula for the nth termis of the form an dn c. Moreover, because the common difference is d 3,the formula must have the forman 3n c.Substitute 3 for d.Because a1 2, it follows thatc a1 d 2 3Substitute 2 for a1 and 3 for d. 1.1 less an a1 n 1 dAlternative formnth term1 lessSo, the formula for the nth term isan 3n 1.The sequence therefore has the following form.2, 5, 8, 11, 14, . . . , 3n 1, . . .Now try Exercise 21.As an aid to learning the formula for thenth term of an arithmetic sequence,consider having your studentsintuitively find the nth term of each ofthe following sequences.1. 5, 8, 11, 14, 17, . . .Answer: 3n 22. a, a 2, a 4, a 6, . . .Answer: 2n a 2Another way to find a formula for the nth term of the sequence in Example2 is to begin by writing the terms of the sequence.a122a22 35a35 38a48 311a511 314a614 317a717 320From these terms, you can reason that the nth term is of the forman dn c 3n 1.
333202 0902.qxd12/5/0511:29 AMPage 655Section 9.2Example 3You can find a1 in Example 3 byusing the alternative recursionform of the nth term of anarithmetic sequence, as follows.an a1 n 1 da4 a1 4 1 d20 a1 4 1 520 a1 155 a1Arithmetic Sequences and Partial Sums655Writing the Terms of an Arithmetic SequenceThe fourth term of an arithmetic sequence is 20, and the 13th term is 65. Writethe first 11 terms of this sequence.SolutionYou know that a4 20 and a13 65. So, you must add the common differenced nine times to the fourth term to obtain the 13th term. Therefore, the fourth and13th terms of the sequence are related bya13 a4 9d.a4 and a13 are nine terms apart.Using a4 20 and a13 65, you can conclude that d 5, which implies thatthe sequence is as 1 . . .55 . . .Now try Exercise 37.If you know the nth term of an arithmetic sequence and you know thecommon difference of the sequence, you can find the n 1 th term by using therecursion formulaan 1 an d.Recursion formulaWith this formula, you can find any term of an arithmetic sequence, provided thatyou know the preceding term. For instance, if you know the first term, you canfind the second term. Then, knowing the second term, you can find the third term,and so on.Example 4Using a Recursion FormulaFind the ninth term of the arithmetic sequence that begins with 2 and 9.SolutionFor this sequence, the common difference is d 9 2 7. There are two waysto find the ninth term. One way is simply to write out the first nine terms (byrepeatedly adding 7).2, 9, 16, 23, 30, 37, 44, 51, 58Another way to find the ninth term is to first find a formula for the nth term.Because the first term is 2, it follows thatc a1 d 2 7 5.Therefore, a formula for the nth term isan 7n 5which implies that the ninth term isa9 7 9 5 58.Now try Exercise 45.
333202 0902.qxd65612/5/05Chapter 911:29 AMPage 656Sequences, Series, and ProbabilityThe Sum of a Finite Arithmetic SequenceThere is a simple formula for the sum of a finite arithmetic sequence.The Sum of a Finite Arithmetic SequenceNote that this formula worksonly for arithmetic sequences.The sum of a finite arithmetic sequence with n terms isnSn a1 an .2For a proof of the sum of a finite arithmetic sequence, see Proofs in Mathematicson page 723.Example 5Finding the Sum of a Finite Arithmetic SequenceFind the sum: 1 3 5 7 9 11 13 15 17 19.SolutionTo begin, notice that the sequence is arithmetic (with a common difference of 2).Moreover, the sequence has 10 terms. So, the sum of the sequence isnSn a1 an Formula for the sum of an arithmetic sequence210 1 19 Substitute 10 for n, 1 for a1, and 19 for an.2 5 20 100.Simplify.The Granger CollectionNow try Exercise 63.Historical NoteA teacher of Carl FriedrichGauss (1777–1855) asked himto add all the integers from 1to 100. When Gauss returnedwith the correct answer afteronly a few moments, theteacher could only look at himin astounded silence. This iswhat Gauss did:1 2 3 . . . 100Sn 100 99 98 . . . 12Sn 101 101 101 . . . 101Sn Sn 100 101 50502Example 6Finding the Sum of a Finite Arithmetic SequenceFind the sum of the integers (a) from 1 to 100 and (b) from 1 to N.Solutiona. The integers from 1 to 100 form an arithmetic sequence that has 100 terms.So, you can use the formula for the sum of an arithmetic sequence, as follows.Sn 1 2 3 4 5 6 . . . 99 100n a1 an Formula for sum of an arithmetic sequence2100 1 100 Substitute 100 for n, 1 for a1, 100 for an.2 50 101 5050Simplify.b. Sn 1 2 3 4 . . . Nn a1 an Formula for sum of an arithmetic sequence2N 1 N Substitute N for n, 1 for a1, and N for an.2Now try Exercise 65.
333202 0902.qxd12/5/0511:29 AMPage 657Section 9.2Arithmetic Sequences and Partial Sums657The sum of the first n terms of an infinite sequence is the nth partial sum.The nth partial sum can be found by using the formula for the sum of a finitearithmetic sequence.Example 7Finding a Partial Sum of an Arithmetic SequenceFind the 150th partial sum of the arithmetic sequence5, 16, 27, 38, 49, . . . .SolutionFor this arithmetic sequence, a1 5 and d 16 5 11. So,c a1 d 5 11 6and the nth term is an 11n 6. Therefore, a150 11 150 6 1644, andthe sum of the first 150 terms isnS150 a1 a150 2 150 5 1644 2nth partial sum formulaSubstitute 150 for n, 5 for a1, and 1644 for a150. 75 1649 Simplify. 123,675.nth partial sumNow try Exercise 69.ApplicationsExample 8Prize MoneyIn a golf tournament, the 16 golfers with the lowest scores win cash prizes. Firstplace receives a cash prize of 1000, second place receives 950, third placereceives 900, and so on. What is the total amount of prize money?SolutionThe cash prizes awarded form an arithmetic sequence in which the commondifference is d 50. Becausec a1 d 1000 50 1050you can determine that the formula for the nth term of the sequence isan 50n 1050. So, the 16th term of the sequence isa16 50 16 1050 250, and the total amount of prize money isS16 1000 950 900 . . . 250nnth partial sum formulaS16 a1 a16 2 16 1000 250 2 8 1250 10,000.Substitute 16 for n, 1000 for a1, and 250 for a16.Simplify.Now try Exercise 89.
333202 0902.qxd65812/5/05Chapter 911:30 AMPage 658Sequences, Series, and ProbabilityExample 9Activities1. Determine which of the following arearithmetic sequences.(a) 3, 5, 7, 9, 11, . . .(b) 3, 6, 12, 24, 48, . . .(c) 3, 6, 9, 12, 15, . . .(d) 5, 0, 5, 10, 15, . . .(e) 1, 3, 6, 10, 15, 21, . . .Answer: (a) and (d)2. Find the first five terms of the arithmetic sequence with a1 13 andd 4.Answer: 13, 9, 5, 1, 33. Find the sum.100 2 3n Total SalesA small business sells 10,000 worth of skin care products during its first year.The owner of the business has set a goal of increasing annual sales by 7500 eachyear for 9 years. Assuming that this goal is met, find the total sales during thefirst 10 years this business is in operation.SolutionThe annual sales form an arithmetic sequence in which a1 10,000 andd 7500. So,c a1 d 10,000 7500 2500and the nth term of the sequence isn 1an 7500n 2500.Answer: 15,350This implies that the 10th term of the sequence isa10 7500 10 2500Sales (in dollars)an80,000 77,500.Small BusinessThe sum of the first 10 terms of the sequence isa n 7500n 250060,000nS10 a1 a10 240,00020,000n 1 2 3 4 5 6 7 8 9 10YearFIGURESee Figure 9.4.9.4nth partial sum formula10 10,000 77,500 2Substitute 10 for n, 10,000 for a1, and 77,500 for a10. 5 87,500 Simplify. 437,500.Simplify.So, the total sales for the first 10 years will be 437,500.Now try Exercise 91.WRITING ABOUTMATHEMATICSNumerical Relationships Decide whether it is possible to fill in the blanks in eachof the sequences such that the resulting sequence is arithmetic. If so, find arecursion formula for the sequence.a. 7,b. 17,c. 2, 6,,,,,,,,, 11,,,,, 71, 162d. 4, 7.5,e. 8, 12,,,,,,,, 60.75,,,,, 39
333202 0902.qxd12/5/0511:30 AMPage 659Section 9.29.2Arithmetic Sequences and Partial Sums659ExercisesVOCABULARY CHECK: Fill in the blanks.1. A sequence is called an sequence if the differences between two consecutive terms arethe same. This difference is called the difference.2. The nth term of an arithmetic sequence has the form .n3. The formula Sn a1 an can be used to find the sum of the first n terms of an arithmetic sequence,2called the of a .PREREQUISITE SKILLS REVIEW: Practice and review algebra skills needed for this section at www.Eduspace.com.In Exercises 1–10, determine whether the sequence isarithmetic. If so, find the common difference.1. 10, 8, 6, 4, 2, . . .2. 4, 7, 10, 13, 16, . . .3. 1, 2, 4, 8, 16, . . .4. 80, 40, 20, 10, 5, . . .97 3 55. 4, 2, 4, 2, 4, . . .536. 3, 2, 2, 2, 1, . . .7.1 23, 3,1,4 53, 6,. . .28. a1 4, a5 1629. a3 94, a6 8530. a5 190, a10 115In Exercises 31–38, write the first five terms of thearithmetic sequence.31. a1 5, d 68. 5.3, 5.7, 6.1, 6.5, 6.9, . . .9. ln 1, ln 2, ln 3, ln 4, ln 5, . . .10. 12, 22, 32, 42, 52, . . .332. a1 5, d 433. a1 2.6, d 0.434. a1 16.5, d 0.25In Exercises 11–18, write the first five terms of the sequence.Determine whether the sequence is arithmetic. If so, findthe common difference. (Assume that n begins with 1.)35. a1 2, a12 4611. an 5 3n12. an 100 3n13. an 3 4 n 2 14. an 1 n 1 438. a3 19, a15 1.715. an 1 n16. an 2n 1 1 n3n18. an 2n n17. an 36. a4 16, a10 4637. a8 26, a12 42In Exercises 39–44, write the first five terms of thearithmetic sequence. Find the common difference andwrite the nth term of the sequence as a function of n.39. a1 15,ak 1 ak 440. a1 6,ak 1 ak 541. a1 200,ak 1 ak 10In Exercises 19–30, find a formula for an for the arithmeticsequence.42. a1 72,19. a1 1, d 344. a1 0.375,543. a1 8,ak 1 ak 6ak 1 ak 18ak 1 ak 0.2520. a1 15, d 421. a1 100, d 822. a1 0, d 23In Exercises 45–48, the first two terms of the arithmeticsequence are given. Find the missing term.23. a1 x, d 2x45. a1 5, a2 11, a10 24. a1 y, d 5y3725. 4, 2, 1, 2 , . . .47. a1 4.2, a2 6.6, a7 26. 10, 5, 0, 5, 10, . . .27. a1 5, a4 1546. a1 3, a2 13, a9 48. a1 0.7, a2 13.8, a8
333202 0902.qxd12/5/0566011:30 AMChapter 9Page 660Sequences, Series, and ProbabilityIn Exercises 49–52, match the arithmetic sequence with itsgraph. [The graphs are labeled (a), (b), (c), and (d).]an(a)2481861246 662 2468 10an3082461841226246 6 1000 5n n 08 3n16n 010078. 2008 250 3i 80. 4.5 0.025j j 1Job Offer In Exercises 81 and 82, consider a job offer withthe given starting salary and the given annual raise.2468 10In Exercises 53–56, use a graphing utility to graph the first10 terms of the sequence. (Assume that n begins with 1.)54. an 5 2n56. an 0.3n 8In Exercises 57– 64, find the indicated nth partial sum of thearithmetic sequence.n 10n 2559. 4.2, 3.7, 3.2, 2.7, . . . ,n 1260. 0.5, 0.9, 1.3, 1.7, . . . ,n 1061. 40, 37, 34, 31, . . . ,76.i 152. an 25 3n58. 2, 8, 14, 20, . . . , 1000 n 50 2n 5 60351. an 2 4 n57. 8, 20, 32, 44, . . . ,2075.79.50. an 3n 555. an 0.2n 3n 1n 1 349. an 4 n 853. an 15 n 51n8 1032n74.n 477.2n 1n 2 2n 1 100an(d)1050 n n250n 1 4(c)n 1100In Exercises 75–80, use a graphing utility to find the partialsum.n872.n 124n 1173.n210 n n400an(b)3071.n 1062. 75, 70, 65, 60, . . . ,n 2563. a1 100, a25 220,n 2564. a1 15, a100 307,n 100(a) Determine the salary during the sixth year ofemployment.(b) Determine the total compensation from the companythrough six full years of employment.Starting SalaryAnnual Raise81. 32,500 150082. 36,800 175083. Seating Capacity Determine the seating capacity of anauditorium with 30 rows of seats if there are 20 seats in thefirst row, 24 seats in the second row, 28 seats in the thirdrow, and so on.84. Seating Capacity Determine the seating capacity of anauditorium with 36 rows of seats if there are 15 seats in thefirst row, 18 seats in the second row, 21 seats in the thirdrow, and so on.85. Brick Pattern A brick patio has the approximate shape ofa trapezoid (see figure). The patio has 18 rows of bricks.The first row has 14 bricks and the 18th row has 31 bricks.How many bricks are in the patio?3165. Find the sum of the first 100 positive odd integers.1466. Find the sum of the integers from 10 to 50.FIGURE FORIn Exercises 67–74, find the partial sum.5067. n10068.n 110069. 6nn 10 2nn 110070. 7nn 5185FIGURE FOR8686. Brick Pattern A triangular brick wall is made by cuttingsome bricks in half to use in the first column of every otherrow. The wall has 28 rows. The top row is one-half brickwide and the bottom row is 14 bricks wide. How manybricks are used in the finished wall?
333202 0902.qxd12/5/0511:30 AMPage 661Section 9.287. Falling Object An object with negligible air resistance isdropped from a plane. During the first second of fall, theobject falls 4.9 meters; during the second second, it falls14.7 meters; during the third second, it falls 24.5 meters;during the fourth second, it falls 34.3 meters. If thisarithmetic pattern continues, how many meters will theobject fall in 10 seconds?88. Falling Object An object with negligible air resistance isdropped from the top of the Sears Tower in Chicago at aheight of 1454 feet. During the first second of fall, theobject falls 16 feet; during the second second, it falls48 feet; during the third second, it falls 80 feet; during thefourth second, it falls 112 feet. If this arithmetic patterncontinues, how many feet will the object fall in 7 seconds?89. Prize Money A county fair is holding a baked goodscompetition in which the top eight bakers receive cashprizes. First places receives a cash prize of 200, secondplace receives 175, third place receives 150, and so on.(a) Write a sequence an that represents the cash prizeawarded in terms of the place n in which the bakedgood places.(b) Find the total amount of prize money awarded at thecompetition.90. Prize Money A city bowling league is holding atournament in which the top 12 bowlers with the highestthree-game totals are awarded cash prizes. First place willwin 1200, second place 1100, third place 1000, andso on.(a) Write a sequence an that represents the cash prizeawarded in terms of the place n in which the bowlerfinishes.(b) Find the total amount of prize money awarded at thetournament.Arithmetic Sequences and Partial Sums661(b) Find the total amount of interest paid over the term ofthe loan.94. Borrowing Money You borrowed 5000 from yourparents to purchase a used car. The arrangements of theloan are such that you will make payments of 250 permonth plus 1% interest on the unpaid balance.(a) Find the first year’s monthly payments you will make,and the unpaid balance after each month.(b) Find the total amount of interest paid over the term ofthe loan.Model It95. Data Analysis: Personal Income The table showsthe per capita personal income an in the United Statesfrom 1993 to 2003. (Source: U.S. Bureau ofEconomic Analysis)YearPer capitapersonal income, an19931994199519961997199819992000200120022003 21,356 22,176 23,078 24,176 25,334 26,880 27,933 29,848 30,534 30,913 31,63391. Total Profit A small snowplowing company makes aprofit of 8000 during its first year. The owner of thecompany sets a goal of increasing profit by 1500 eachyear for 5 years. Assuming that this goal is met, find thetotal profit during the first 6 years of this business. Whatkinds of economic factors could prevent the company frommeeting its profit goal? Are there any other factors thatcould prevent the company from meeting its goal? Explain.(a) Find an arithmetic sequence that models the data.Let n represent the year, with n 3 correspondingto 1993.92. Total Sales An entrepreneur sells 15,000 worth of sportsmemorabilia during one year and sets a goal of increasingannual sales by 5000 each year for 9 years. Assuming thatthis goal is met, find the total sales during the first 10 yearsof this business. What kinds of economic factors couldprevent the business from meeting its goals?(c) Use a graphing utility to graph the terms of thefinite sequence you found in part (a).93. Borrowing Money You borrowed 2000 from a friend topurchase a new laptop computer and have agreed to payback the loan with monthly payments of 200 plus 1%interest on the unpaid balance.(a) Find the first six monthly payments you will make, andthe unpaid balance after each month.(b) Use the regression feature of a graphing utility tofind a linear model for the data. How does thismodel compare with the arithmetic sequence youfound in part (a)?(d) Use the sequence from part (a) to estimate the percapita personal income in 2004 and 2005.(e) Use your school’s library, the Internet, or someother reference source to find the actual per capitapersonal income in 2004 and 2005, and comparethese values with the estimates from part (d).
333202 0902.qxd66212/8/0510:53 AMChapter 9Page 662Sequences, Series, and Probability96. Data Analysis: Revenue The table shows the annualrevenue an (in millions of dollars) for NextelCommunications, Inc. from 1997 to 2003. (Source:Nextel Communications, Inc.)(d) Compare the slope of the line in part (b) with thecommon difference of the sequence in part (a). Whatcan you conclude about the slope of a line and thecommon difference of an arithmetic sequence?102. Pattern RecognitionYearRevenue, 72110,820(a) Compute the following sums of positive odd integers.1 3 1 3 5 1 3 5 7 1 3 5 7 9 1 3 5 7 9 11 (b) Use the sums in part (a) to make a conjecture about thesums of positive odd integers. Check your conjecturefor the sum1 3 5 7 9 11 13 .(a) Construct a bar graph showing the annual revenuefrom 1997 to 2003.(c) Verify your conjecture algebraically.(b) Use the linear regression feature of a graphing utilityto find an arithmetic sequence that approximates theannual revenue from 1997 to 2003.103. Think About It The sum of the first 20 terms of anarithmetic sequence with a common difference of 3 is 650.Find the first term.(c) Use summation notation to represent the total revenuefrom 1997 to 2003. Find the total revenue.104. Think About It The sum of the first n terms of an arithmetic sequence with first term a1 and common differenced is Sn. Determine the sum if each term is increased by 5.Explain.(d) Use the sequence from part (b) to estimate the annualrevenue in 2008.SynthesisSkills ReviewTrue or False? In Exercises 97 and 98, determine whetherthe statement is true or false. Justify your answer.In Exercises 105–108, find the slope and y-intercept (ifpossible) of the equation of the line. Sketch the line.97. Given an arithmetic sequence for which only the first twoterms are known, it is possible to find the nth term.105. 2x 4y 398. If the only known information about a finite arithmeticsequence is its first term and its last term, then it ispossible to find the sum of the sequence.107. x 7 099. Writing In your own words, explain what makes asequence arithmetic.In Exercises 109 and 110, use Gauss-Jordan elimination tosolve the system of equations.100. Writing Explain how to use the first two terms of anarithmetic sequence to find the nth term.106. 9x y 8108. y 11 0109.101. Exploration(a) Graph the first 10 terms of the arithmetic sequencean 2 3n.(b) Graph the equation of the line y 3x 2.110. 2x y 7z 103x 2y 4z 176x 5y z 20 x 4y 10z 45x 3y z 318x 2y 3z 5(c) Discuss any differences between the graph ofan 2 3nand the graph ofy 3x 2.111. Make a Decision To work an extended applicationanalyzing the median sales price of existing one-familyhomes in the United States from 1987 to 2003, visit thistext’s website at college.hmco.com. (Data Source:National Association of Realtors)
Arithmetic sequences have practical real-life applications. For instance,in Exercise 83 on page 660,an arithmetic sequence is used to model the seating capacity of an auditorium. . arithmetic sequence may be thought of as a li
3.2 Arithmetic series: the sum of an arithmetic sequence Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life. 7C 7D Arithmetic Sequence Arithmetic Series 6C 6D Arithmetic sequences Arithmetic series 3.1 3.2 Arithmetic sequence Arithmetic s
Algebra I Unit 10: Arithmetic & Geometric Sequences Math Department TEKS: A.12D 2015 - 2016 Arithmetic Sequences Objectives Students will be able to identify if a sequence is arithmetic. Students will be able to determine the value of a specific term. Students will be able to write arithmetic sequences in explicit form.
arithmetic sequence are called arithmetic means. In the sequence below, 38 and 49 are the arithmetic means between 27 and 60. 5, 16, 27, 38 , 49 , 60 760 Chapter 12 Sequences and Series The n th term of an arithmetic sequence with first term a 1 and common difference d is given by a n a 1 (n 1) d . The n th Term of an Arithmetic Sequence .
Arithmetic & Geometric Sequences Worksheet Level 2: Goals: Identify Arithmetic and Geometric Sequences Find the next term in an arithmetic sequence Find the next term in a geometric sequence Practice #1 Does this pattern represent an arithmetic or geometric sequence? Explain. Find how many dots would be in the next figure?
Arithmetic & Geometric Sequences Worksheet Level 2: Goals: Identify Arithmetic and Geometric Sequences Find the next term in an arithmetic sequence Find the next term in a geometric sequence Practice #1 Does this pattern represent an arithmetic or geometric sequence? Explain. Find how many dots would be in the next figure?
arithmetic sequence finds the nth term of an arithmetic sequence lists down the first few terms of an arithmetic sequence given the general term and vice-versa solves word problems involving arithmetic mean applies the concepts of mean and the nth term of an arithmetic sequence
Arithmetic Series: A series whose terms form an arithmetic sequence. 11 4 Arithmetic Series 7 April 27, 2009 Apr 21 4:18 PM. 11 4 Arithmetic Series 8 April 27, 2009 Apr 21 4:19 PM. 11 4 Arithmetic Series . Homework: page 622 (2 32 even, 37, 40) Title: 11-4 Arithmetic Series Subject: SMART Board Interactive Whiteboard Notes
Unit 11 (Sequences and Series) Day 2: Arithmetic Sequences . 5 The arithmetic mean of any two numbers is the average of two numbers. Some facts: For any three sequential terms in an arithmetic sequence, the middle term is the arithmetic mean of the first and third.
