Chapter 1 BLM - McGraw-Hill Ryerson

Name: ___________________________________________ Date: _____________________________Chapter 1 Prerequisite SkillsBLM 1–21. Determine whether each relation is linear ornon-linear. Justify each answer.a) A = πr 2b) y = 5x – 3c) (0, 0), (1, 1), (4, 2), (9, 3), (16, 4)d) (2, 5), (4, 10), (6, 15), (8, 20), (10, 25)2. Christina writes the following numberpattern: 9, 16, 23, … .a) Create a table of values for the firstfive terms.b) Develop an equation that can be used todetermine the value of each term in thenumber pattern.c) What is the value of the 71st term?d) Which term has a value of 135?3. Julian creates a number pattern that startswith the number −4. Each subsequent termis 5 less than the previous term.a) Create a table of values for the first fivenumbers in the pattern.b) What equation can be used to representthe pattern? Verify your answerby substituting a known value intoyour equation.c) What is the value of the 49th term?d) Which term has a value of −89?4. Create a graph and a linear equation torepresent each table of values.a) x y–3 –8–2 –5–1 –20 11 42 73 10b) x y12 215 318 421 524 627 730 85. Express each equation in slope-interceptform.a) 2x + y = 6b) 3x + y + 9 = 0c) 5x + 6y = 8d) 6x – y = 4e) 7x – y + 9 = 0f) 8x – 4y = 3Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________BLM 1–2(continued)6. What is the value of each expression?a) 5 3b) (−6) 44⎛1⎞c) ⎜2⎟⎝ ⎠⎛ 2 ⎞d) ⎜−3⎟⎝ ⎠7. Evaluate.a) 3 − 8b) 4 81c)⎛1⎞⎜ ⎟⎝9⎠2⎛ 32 ⎞d) 5⎜−⎟⎝ 243 ⎠9. Protactinium has a half-life of 2 min.Suppose a sample of protactinium has amass of 1000 g. The formula for the massof protactinium remaining after n 2-minintervals is A = 1000 1 n⎛ ⎞⎜2⎟⎝ ⎠ .a) Create a table of values showing theamount of protactinium remainingafter the first five 2-min intervals.b) How long would it take for the sample tobe reduced to 1 th its original size?648. Simplify each expression by rewriting itusing positive exponents only.312a)7121b)2 −3s t8tc)−3td) ⎡ 5( xy )⎢⎣−3−2⎤⎥⎦Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Chapter 1 Warm-UpSection 1.1 Warm-Up1. Describe the pattern demonstrated by eachof the following.a) 2, 4, 6, 8, …b) 1, 4, 7, 10, …c) 5, 11, 17, …2. Solve for x.a) 35 = 3x – 4b) 64 = –2(x – 3)3. If g(n) = 6n – 11, determinea) g(1)b) g(0)c) g(–3)BLM 1–34. For each system of linear equations, useelimination or addition to solve for x.a) 22 = 2x – y12 + 2x = 3yb) 7 = 1 2 x + 1 2 y–10 – x = 2y5. Consider the equation y = 4x – 1.a) Determine the slope and y-intercept ofthe line.b) Create a table of values for values of xfrom 0 to 5.Section 1.2 Warm-Up1. Identify whether each of the following is anarithmetic sequence. If so, state the values 4. Solve the following linear system for xof t 1 and d.and y.2y – 3x = 5 and 3y = –5x + 1a) 2, 4, 6, …b) –5, 10, –20 …5. Copy each diagram into your notebookc) 1, 4, 7, …and sketch the resulting rotations about thepoint C.d) –6, –1, 4, …a)2. For t n = t 1 + (n – 1)d,a) explain the meaning of t n , t 1 , n, and db) determine t 26 for 3, 6, 9, …c) determine t 1 if t 30 = 82 and d = 3d) write the general form for 2, 6, 10, …3. Simplify each equation.b)a) y = 2[3(x – 1) + 3]b) y = 1 [4(x + 2) – 6]2c) y = 2 3 (27 + 54x)Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

BLM 1–3(continued)Section 1.3 Warm-Up1. Determine whether each pattern representsan arithmetic sequence. If it does, state thevalue of t 1 and d. If it does not represent anarithmetic sequence, explain why.a) 2, 4, 6, …b) 2, 4, 8, …c) 5, 3, 1, …d) –4, –2, –1, …2. For the arithmetic sequence –6, –3, 0, …,a) what is the general term t n ?b) determine S 10 .3. A 20 cm × 16 cm photograph of a companylogo is being used for advertisements.Determine the new dimensions if thephotograph needs to bea) enlarged 240% to create a poster.b) reduced by 25% to fit in a book.4. Use technology to determine each value tothe nearest hundredth.a) 3 45b) 7 16c) 25 28 7123d) 3 125 = 7 s5. a) Using elimination, solve for r in thefollowing system.4r + s = 102r + s = –44b) Using substitution, solve for r in thefollowing system.4s = r33s + r = 256Section 1.4 Warm-Up1. Determine whether each sequence isarithmetic, geometric, or neither.a) 0.6, 0.66, 0.666, …b) 5, 6, 7, …c) 4, –4, 4, …d) 1 , 1 , 1 , ...4 16 64e)17 12 7, , , ...5 5 52. For each sequence,• determine r.• write the next two terms.• determine the general term t n .a) 2, –6, 18, …−10 20 −40b) 5, , , , ...3 9 273. What is n in the sequence2, 14, 98, , 4802? Justify your work.4. What is r in each of the following?1 4a) 125 = r51 1 1b) 1, , , ,6 36 77765. If t 2 = 28 and t 5 = 1792, what are the valuesof t 1 , r, and t n ?Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

BLM 1–3(continued)Section 1.5 Warm-Up1. Identify whether each series is arithmeticor geometric. Then, determine S 18 to thenearest tenth, if appropriate.5a) 3 + + 2 + ...23 3b) 3 + + + ...2 4c) 10 + 13 + 16 + …d) 12 + 24 + 48 + …2. Consider the series1 1 1 11 − + − + + .3 9 27 59 049a) Determine t 1 , r, and n.b) Write the general form for t n .c) Determine the sum of the series,to the nearest hundredth.3. Draw a 6 cm line and label the endpoints Aand B. Locate the midpoint betweenpoints A and B and label it C. Locate themidopoint between points A and C and labelit D. Suppose this process continues withpoints E and F, respectively.a) Write a sequence that represents theprocess.b) If the next point is included, determinethe length of segment AG.4. Write each fraction as a repeating decimal.a) 2 9b) 239947c)9995. Simplify. Express each answer in fractionform.a)3⎛4⎞24⎜ −5⎟⎝ ⎠2⎛1⎞b) − 15⎜ +6⎟⎝ ⎠236. Evaluate. Express each answer to thenearest hundredth.⎛1⎞a) ⎜2⎟⎝ ⎠⎛1⎞b) ⎜2⎟⎝ ⎠c)468⎛1⎞⎜2⎟⎝ ⎠Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________Section 1.1 Extra PracticeBLM 1–41. Identify which of the following sequencesare arithmetic. For each arithmeticsequence, state the values of t 1 and d,and the next three terms.a) 4, 7, 10, 13, …b) 12, 7, 2, –3, …c) 5, 15, 45, 135, …d) x, x 2 , x 3 , x 4 , …e) x, x + 2, x + 4, x + 6, …2. Write the first four terms of each arithmeticsequence for the given values of t 1 and d.a) t 1 = –5, d = –2b) t 1 = 10, d = –0.5c) t 1 = 3, d = xd) t 1 = 7 3 , d = 1 33. Given the general term, state the first fourterms of each sequence. Then, graph t nversus n.a) t n = 13 – 3nb) t n = 1 2 n + 44. Determine the general term and the 50thterm for each arithmetic sequence.a) 6, 10, 14, …b) 3, 2 1 2 , 2, …5. Determine the number of terms in eachfinite arithmetic sequence.a) –6, –3, 0, … , 222b) 3 1 4 , 3 3 4 , 4 1 4 , … , 15 3 46. Determine the unknown terms in eacharithmetic sequence.a) 4, , , 16b) , 8, , , 2c) 20, , , , , –107. The 20th term of an arithmetic sequence is107, and the common difference is 5.Determine the first term, the general term,and the 40th term of this sequence.8. Use the two given terms to find t 1 , d, and t nfor each arithmetic sequence.a) t 11 = 25, t 30 = 101b) t 2 = 90, t 51 = –579. The terms 5 + x, 8, and 1 + 2x areconsecutive terms in an arithmetic sequence.Determine the value of x and state thethree terms.10. The triangular shapes are made fromasterisks.a) How many asterisks will be in the fourthtriangle? the fifth triangle?b) Write the general term for the sequenceinvolving the number of asterisks in thetriangles.c) How many asterisks will be in the20th diagram?d) Which diagram will contain126 asterisks?Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________Section 1.2 Extra PracticeBLM 1–51. Determine the sum of each arithmetic series.a) 14 + 10 + 6 + + (–86)b) 5 + 6.5 + 8 + + 26c) 3 4 + 2 + 13 4 + + 49 22. For each arithmetic series, determine theindicated sum.a) 4 + 9 + 14 + …; first 12 termsb) (–16) + (–14) + (–12) + …; first 17 termsc) x + 3x + 5x + …; first 20 terms3. For each arithmetic series, determine thenumber of terms.a) 3 + 7 + 11 + + t n = 465b) –2 – 5 – 8 – – t n = –950c) t 1 = 20, t n = –40, S n = –2104. For each arithmetic series, determine the12th term and the 12th partial sum.a) 3 – 1 – 5 – …b) 3 5 + 7 5 + 11 5 + …6. Determine the sum of all multiples of 7between 1 and 1000.7. In an arithmetic series, the third term is 24and the sixth term is 51. What is the sum ofthe first 25 terms of the series?8. The sum of the first eight terms of anarithmetic series is 176. The sum of the firstnine terms is 216. Determine the first andninth terms of the series.9. The sum of the first n terms of an arithmeticseries is S n = 3n 2 + 4n.a) Determine the first five partial sums.b) Determine the first five terms of theseries.c) Use the formula to verify that the sum ofthe first five terms is equal to S 5 .10. A student is offered the opportunity to earn$6.00 for the first day, $11.00 for the secondday, $16.00 for the third day, and so on,for 20 working days. Or, the student canaccept $1000 for the whole job. Which offerpays more?5. Determine the sum of each arithmetic series,given the first and nth terms.a) t 1 = –3, t 14 = 62b) t 1 = 3 , t 10 = 18 3Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________Section 1.3 Extra PracticeBLM 1–61. Is each sequence geometric? If it is, state thecommon ratio and a formula to determinethe general term in the form t n = t 1 r n – 1 .a) 11, 33, 99, 297, …b) 6, 12, 18, 24, …c) 1 , 2 , 4 , 8 , …3 3 3 3d) 0.5, 0.2, 0.08, 0.032, …2. Write the first four terms of each geometricsequence.a) t 1 = 7, r = –3b) t 1 = –8, r = 1 2c) t n = 3(0.6) n – 1d) t n = (–4) n3. Determine the number of terms in eachgeometric sequence.a) 4, 12, 36, , 78 732b) 5 2 , 10, 10 2 , , 640c) t 1 = 5, r =1− , t n = 5 2 64d) t 1 = 1 4 , r = 3, t n = 44 286.754. Determine the nth term of each geometricsequence.a) t 1 = 2, r = 7b) 6, –18, 54, –164, …c) t 1 = 7, t 5 = 1792d) r = 1 4 , t 8 = 1 45. Determine the unknown terms in eachgeometric sequence.a) 18, , , 6174b) , 4, , , 108c) 5, , , , 806. The first term of a geometric sequence is0.1; the tenth term is 26 214.4. Determinethe value of the common ratio.7. Determine the first term, the common ratio,and an expression for the general term ofeach geometric sequence.a) t 5 = 900, t 7 = 0.09b) t 3 = –1728, t 6 = 373 248c) t 5 = 28, t 11 = 1792d) t 2 = 3, t 4 = 0.758. The following sequences are geometric.What is the value of each variable?a) 8x – 12, 16, 64, 256, …b) 25, 5, 1, 2y – 1, …9. For a geometric sequence t 4 = 4x + 8 andt 7 = x – 4. If the common ratio is 1 , what is2the first term?10. An excavating company has a digger thatwas purchased for $240 000. It isdepreciating at 12% per year.a) Determine the next three terms of thisgeometric sequence.b) Determine the general term. Define yourvariables.c) How much will the digger be worth in7 years?d) How long will it take before theequipment is worth less than$120 000?Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________Section 1.4 Extra PracticeBLM 1–71. Determine whether each series is geometric.Justify your answers.a) 5 + 6 + 7.2 + 8.64 + …b) 3125 – 625 + 125 – 25 + …c) 3 + 1 + 1 + 2 +…4 2 3 9d) 2 + 3 + 5 + 8 + …2. For each geometric series, state thevalues of t 1 and r. Then, determine eachpartial sum.a) 0.43 + 0.0043 + 0.000 043 + …, (S 6 )b) 5 – 5 + 5 – …, (S 10 )c) –100 + 50 – 25 + …, (S 7 )3. Determine the partial sum, S n , for eachgeometric series described.a) t 1 = 50, r = 1.1, n = 4b) t 1 = –4, r = 2, n = 10c) t n = (–5)(0.5) n – 1 , n = 5d) t n = (3)(2) n – 1 , n = 124. Determine the partial sum, S n , for eachgeometric series.a) 2 + 6 + 18 + + 354 294b) t 1 = –3, r = –2, t n = 6144c) S n = (–32)(0.75 n – 1), n = 65. Determine the first term for each geometricseries.a) S n = 3932.4, t n = 4915.2, r = –4b) S n = 292 968, n = 8, r = 56. Determine the number of terms in eachgeometric series.a) 4 + 20 + 100 + + t n = 15 624b) 1792 – 896 + 448 – – t n = 11977. The fourth term of a geometric series is 30;the ninth term is 960. Determine the sum ofthe first nine terms.8. The first term of a geometric sequence is 3.The sum of the first two terms of the series is15 and the sum of the first three terms of theseries is 63. Determine the common ratio.9. Determine the first four terms of eachgeometric series.a) S n = 5(3 n – 1)b) S n = –24(0.5 n – 1)10. A ball is dropped from the top of a25-m ladder. In each bounce, the ballreaches a vertical height that is 3 5 theprevious vertical height. Determine the totalvertical distance travelled by the ball whenit contacts the ground for the sixth time.Express your answer to the nearest tenthof a metre.Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________Section 1.5 Extra PracticeBLM 1–81. State whether each geometric series isconvergent or divergent.a) 80 + 20 + 5 + 5 4 + …b) –30 + 20 – 40 3 + 80 9 – …c) t 1 = –5, r = 1 2d) t 1 = 1 3 , r = –22. Determine the sum of each geometric series,if it exists.a) t 1 = –4, r = 4 5b) t 1 = 10, r =−23c) 10 + 10 3 + 30 + 30 3 + …d) 5 − 5 + 5 −5 + …3 9 27 81e) 8 + 8 2 23⎛ ⎞⎜3⎟⎝ ⎠ + 8 ⎛2⎞⎜3⎟⎝ ⎠ + 8 ⎛2⎞⎜3⎟⎝ ⎠ + …23⎛−3⎞f) – 2 – 2 ⎜4⎟⎝ ⎠ – 2 ⎛−3⎞⎜4⎟⎝ ⎠ – 2 ⎛−3⎞⎜4⎟⎝ ⎠ – …3. Express each of the following as an infinitegeometric series. Determine the sum ofthe series.a) 0.63b) 7.45c) 0.123 4564. The general term of an infinite geometricn−1⎛1⎞series is t n= 7 ⎜ 3 ⎟ . Determine the sum of⎝ ⎠the series, if it exists.5. The sum of an infinite geometric series is10and the first term is 5. Determine the3common ratio.6. The sum of an infinite geometric series is3π 1and the common ratio is22 . Determinethe first term.7. A ball is dropped from a height of 2.0 monto a floor. On each bounce the ball risesto 75% of the height from which it fell.Calculate the total distance the ball travelsbefore coming to rest.8. Determine the values of x such that theseries 1 + x + x 2 + x 3 + … has a sum.9. The sum of an infinite geometric series isthree times the first term. Determine thecommon ratio.10. A new oil well produces 12 000 m 3 /monthof oil. Its production is known to bedropping by 2.5% each month.a) What is the total production in thefirst year?b) Determine the total production ofthe well.Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________Chapter 1 TestMultiple ChoiceFor #1 to 5, select the best answer.1. What are the missing terms of the arithmeticsequence 4, , 14, , 24, ?A 10, 20, 30B 9, 19, 29C 5, 10, 15D 8, 18, 282. While baking a cake, Dylan notices thateach of his measuring cups is about half asbig as the one before it. The largest (first)measuring cup is 250 mL. What is theapproximate capacity of the fourthmeasuring cup?A 125 mLB 65 mLC 30 mLD 15 mL3. The years in which the CommonwealthGames take place form an arithmeticsequence with a common difference of 4. In1978, the Commonwealth Games were heldin Edmonton, Alberta. In which of thefollowing years could the CommonwealthGames be held again?A 2011B 2022C 2033D 2044BLM 1–94. The sum of the first 20 terms of thearithmetic series 204 + 212 + 216 + ... isA 11 200B 7120C 5680D 56005. The sum of the first 11 terms of thegeometric series 7 – 14 + 28 – … isA 28 679B 4 781C –9 555D –28 665Short Answer6. Gentry notices that the bank of lockersoutside his math classroom are numbered511, 513, 515, ..., 575. Determine thenumber of lockers in the set.7. Brittany, a landscape designer, is setting outtrees for planting. The 12 trees she needs arecurrently in one location, 40 m from thespot the first tree will be planted. The treeswill be spaced 6 m apart. The cart she usesto transport the trees will only carry one treeat a time, so she must take the first tree to itsspot, return for the second tree, take it to itsspot, and so on. After Brittany takes all12 trees to the correct spot and returns tothe original location of the trees, how farwill she have travelled, in total?Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Name: ___________________________________________ Date: _____________________________BLM 1–9(continued)8. Determine the sum of the arithmetic series9 + 21 + 33 + + 693.9. In an arithmetic sequence, t 3 = 16 andt 7 = 40.a) Determine the common difference in thesequence.b) Determine the first term in the sequence.c) Determine t 100 .10. 5, , 405 is a geometric sequence.a) Determine all possible values for thesecond term of this sequence.b) Determine all possible general termsfor this sequence.11. The nth sum of a sequence is given by theformula S n = 1 – 4 n .a) Determine the first three terms of thesequence.b) Decide whether the sequence isarithmetic or geometric. Determine thegeneral term for the sequence.Extended Response12. Write a geometric series with a positivefirst term.a) Find the sum of the first ten terms ofyour series.b) Change the common ratio of your seriesso the sum of the first ten terms is theopposite sign, but the same value, as inpart a). For example, if your sum waspositive in part a), ensure that it isnegative for part b).c) Create a geometric series so that S n ispositive when n is odd, and S n is negativewhen n is even. Justify your answer.13. According to Statistics Canada,Chestermere, Alberta is one of the fastestgrowing communities in Canada. Between2001 and 2006, the population grew at anaverage rate of about 8% per year.a) The population of Chestermere in 2001was 6462. Determine the population forthe years 2002 through 2004, inclusive.b) Write the general term for the geometricsequence that models the population ofChestermere, where n is the number ofyears starting in 2001.c) Predict the population of Chestermere inthe year 2020.d) What assumption(s) did you make inyour answer to part c)?14. Write a sequence that is both arithmetic andgeometric.a) Prove that your sequence is arithmetic.Determine the general term of thesequence.b) Prove that your sequence is geometric.Determine the general term of thesequence.c) How many sequences could be botharithmetic and geometric? Justify youranswer.Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

Chapter 1 BLM AnswersBLM 1–2 Chapter 1 Prerequisite Skills1. a) Non-linear. Each increase in the value of rincreases the value of A by a different amountb) Linear. Each increase in the value of x increasesthe value of y by the same amount, 5.c) Non-linear. Each increase in the value of the firstcoordinate increases the value of the secondcoordinate by a different amount.d) Linear. The same increase in the value of the firstcoordinate (2) increases the value of the secondcoordinate by the same amount, 5.2. a)Term Number Value1 92 163 234 305 37b) v = 7t + 2 c) 499 d) t = 193. a)Term Number Value1 −42 −93 −144 −195 −24b) v = −5t + 1Substitute t = 3. The result should be −14.v = −5(3) + 1v = −15 + 1v = −14c) −244 d) t = 184. a)y = 3x + 1b)BLM 1–101t = s − 23⎛5⎞45. a) y = −2x + 6 b) y = −3x − 9 c) y =− ⎜ x+6⎟⎝ ⎠ 33d) y = 6x − 4 e) y = 7x + 9 f) y = 2x−46. a) 125 b) 1296 c) 116 or 0.0625 d) 4 97. a) −2 b) 3 c) 1 3 d) 2−331 t8. a) b) c) 8t 4 d) x 6 y 304212 s9. a)Number of2-min Intervalsb) 12 minAmount ofProtactinium0 10001 5002 2503 1254 62.55 31.25BLM 1–3 Chapter 1 Warm-UpSection 1.11. a) The first term is 2. The common difference is 2.b) The first term is 1. The common difference is 3.c) The first term is 5. The common difference is 6.2. a) x = 13 b) x = −293. a) g(1) = −5 b) g(0) = −11 c) g(−3) = −2914. a) x = 19 b) x = 382Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

BLM 1–10(continued)5. a) slope = 4, y-intercept = −1b)x y0 −11 32 73 114 155 19Section 1.21. a) arithmetic sequence, t 1 = 2, d = 2b) not arithmetic sequencec) arithmetic, t 1 = 1, d = 3d) arithmetic, t 1 = −6, d = 52. a) t n is the general term, t 1 is the first term, n is thenumber of terms, and d is the common difference.b) t 26 = 78 c) t 1 = −5 d) t n = 2 + 4(n – 1)3. a) y = 6x b) y = 2x + 1 c) y = 18 + 36x13 844. x = , y =19 575. a) b)Section 1.31. a) arithmetic, t 1 = 2, d = 2b) not arithmetic because you multiply by 2 to findeach successive termc) arithmetic, t 1 = 5, d = −2d) not arithmetic because you multiply by 1 to find2each successive term2. a) t n = 3n – 9 b) S 10 = 753. a) 48 cm × 38.4 cm b) 15 cm × 12 cm4. a) 3.56 b) 1.49 c) 1.51 d) s = 11.675. a) r = 27 b) r = 51.24. a) r = 5 b) r = 1 65. t 1 = 7, r = 4, t n = 7(4) n – 1Section 1.5451. a) arithmetic, S 18 = − or –22.52b) geometric, S 18 = 6.0 c) arithmetic, S 18 = 639d) geometric, S 18 = 3 145 71612. a) t 1 = 1, r = − and n = 113n−1⎛ 1 ⎞b) t n= 1 ⎜ −3 ⎟ c) S 11 = 0.75⎝ ⎠3. a) 6, 3, 3 , 3 ,32 4 8b) The length from A to G would be 3 cm or160.1875 cm.4. a) 0.2 b) 0.23 c) 0.0475. a) 27 343b) −25 5406. a) 0.06 b) 0.02 c) 0.00BLM 1–4 Section 1.1 Extra Practice1. a) arithmetic; t 1 = 4, d = 3; 16, 19, 22b) arithmetic; t 1 = 12, d = –5; –8, –13, –18c) not arithmetic d) not arithmetice) arithmetic; t 1 = x, d = 2; x + 8, x + 10, x + 122. a) –5, –7, –9, –11 b) 10, 9.5, 9, 8.5c) 3, 3 + x, 3 + 2x, 3 + 3x d) 7 , 8 , 9 ,103 3 3 33. a) 10, 7, 4, 1Section 1.41. a) neither b) arithmetic c) geometricd) geometric e) arithmetic2. a) r = –3; –54, 162; t n = 2(–3) n – 1n2 80 −1602b) r = − ; , ; t 5 ⎛ − ⎞n=3 81 243 ⎜ 3 ⎟⎝ ⎠3. Solve 2(7) n – 1 = 4802 to get n = 5.−1Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

BLM 1–10(continued)b) 41, 5, 51, 62. a) 7, –21, 63, –1892 2b) –8, –4, –2, –1c) 3, 1.8, 1.08, 0.648d) –4, 16, –64, 2563. a) 10 b) 14 c) 7 d) 124. a) t n = 2(7) n – 1 b) t n = 6(–3) n – 1n−1c) t n = 7(4) n – 1 ⎛1⎞d) t n = 4096⎜4⎟⎝ ⎠5. a) 126, 882 b) 4 , 12, 36 c) ±10, 20, ±4036. 47. a) t 1 = 9 × 10 10 , r = ±0.01,t n = (9 × 10 10 )(±0.01) n – 1b) t 1 = –48, r = –6, t n = (–48)(–6) n – 1c) t 1 = 1.75, r = ±2, t n = (1.75)(±2) n – 14. a) t n = 4n + 2; t 50 = 202 b) t n = 7 12 − 2 n ;d) t 1 = ±6, r = ±0.5, t n = (6)(±0.5) n – 18. a) x = 2 b) y = 6t 50 = − 21 110 or 3 529. 3845. a) 77 b) 2610. a) $211 200, $185 856, $163 5536. a) 4, 8 , 12 , 16 b) 10 , 8, 6 , 4 , 2b) t n = 240 000(0.88) n – 1 , t n = value of digger,in dollars, n – 1 = years since purchasec) 20, 14, 8, 2, −4, − 10c) $98 082 d) 6 years7. t 1 = 12, t n = 5n + 7, t 40 = 2078. a) t 1 = –15, d = 4, t n = 4n – 19BLM 1–7 Section 1.4 Extra Practiceb) t 1 = 93, d = –3, t n = 96 – 3n10 25 231. a) geometric series, the common ratio is 1.29. x = ; , 8,b) geometric series, the common ratio is –0.23 3 310. a) 15, 18 b) t n = 3n + 3c) geometric series, the common ratio is 2 3c) 63 asterisks d) 41st diagramd) not geometric, no common ratioBLM 1–5 Section 1.2 Extra Practice2. a) t 1 = 0.43, r = 0.01, S 6 = 43991b) t 1 = 5, r = –1, S 10 = 01. a) –936 b) 232.5 c) 252.5 or 252 2c) t 1 = –100, r = –0.5, S 7 =−1075162. a) 378 b) 0 c) 400x3. a) 15 b) 25 c) 213. a) 232.05 b) –4092 c)−155d) 12 2854. a) t 12 = –41, S 12 = –228 b) t 12 = 47 165 , S 12 = 604. a) 531 440 b) 4095 c) 33671285. a) 413 b) 95 35. a) 1.2 b) 36. 71 071 7. 2850 8. t 1 = 8, t 9 = 406. a) 6 b) 99. a) S 1 = 7, S 2 = 20, S 3 = 39, S 4 = 64, S 5 = 957. 1916.25 8. 4b) T 1 = 7, T 2 = 13, T 3 = 19, T 4 = 25, T 5 = 319. a) 10, 30, 90, 270 b) 12, 6, 3, 1.5c) S 5 = 3(5) 2 + 4(5) = 9510. 94.2 m10. 6 + 11 + 16 + + t 20 = $1070. Therefore, thearithmetic series method pays more money.BLM 1–8 Section 1.5 Extra Practice1. a) convergent b) convergent c) convergentBLM 1–6 Section 1.3 Extra Practiced) divergent1. a) geometric, r = 3, t n = 11(3) n – 1b) not geometric c) geometric, r = 2, t n = 1 2. a) –20 b) 6 c) does not exist d) 53 (2)n – 14 e) 24 f) 8−7d) geometric, r = 0.4, t n = (0.5)(0.4) n – 1Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.

BLM 1–10(continued)3. a) 63 + 63 + 63 + =72 3100 (100) (100) 115 5 5 41b) 7.4 + + + + = 7100 1000 10 000 90c)456 456 456 41 1110.123 + + + + = (1000)2 (1000)3 (1000)4 333 0004. 2129. 2 35.1− 6. 3 π 7. 14 m 8. |x| < 12 410. a) 125 761 m 3 b) 480 000 m 3BLM 1–9 Chapter 1 Test1. B 2. C 3. B 4. D 5. B6. There are 33 lockers.7. Brittany travelled 1752 m.8. 20 3589. a) d = 6 b) t 1 = 4 c) t 100 = 59810. a) r = 9 or –9 b) t n = 5(9) n – 1 or t n = 5(–9) n – 111. a) –3, –12, –48b) The sequence is geometric. t n = –3(4) n – 112. a) Example, for the series2 + 10 + 50 + ..., S 10 = 4 882 812.b) Answers will vary. Students need to change thesign of the first term, while leaving the common ratiounchanged. In the example above, the series becomes–2 – 10 – 50 – ..., S 10 = 4 882 812.c) Answers will vary. Correct answers must havepositive first term and negative common ratio.For example, 2 – 10 + 50 – ….13. a) 6979, 7537, 8140 b) t n = 6462(1.08) n – 1c) 27 888d) Answers will vary. For example, we assume thatpopulation continues to grow at the same rate.14. Answers will vary, however will all be in theform k, k, k, …, where k is a real number.a) Note that d = 0, so t n = k.b) Note that r = 1, so t n = k.c) There are infinitely many such sequences, but allsequences will have the same form.Copyright © 2010, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. All rights reserved.This page may be reproduced for classroom use by the purchaser of this book without written permission of the publisher.