Lesson 1.1 Recursively Defined Sequences

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1 Lesso 1.1 Recursively Defied Sequeces 1. Tell whether each sequece is arithmetic, geometric, or either. a. 1,, 9, 13,... b. 2, 6, 18, 4,... c. 1, 1, 2, 3,, 8,... d. 16, 4, 1,.2,... e. 1, 1, 1, 1,... f..6, 2.8,, 2.8, Fid the commo differece, d, for each arithmetic sequece ad the commo ratio, r, for each geometric sequece. a. 6, 11, 16, 21,... b. 1, 1, 1,.1,... c. 1., 1.,.,,.,... d..62,.12,.2,... e. 1,.2,.4,.8,... f. 4, 3.99, 3.98, Write the first six terms of each sequece, startig with u 1. a. u 1 18 b. u where where 2 c. u d. u where where 2 4. Write a recursive formula to geerate each sequece. The fid the idicated term. a. 1, 11, 7, 3,... Fid the 1th term. b. 1, 1, 1, 1,... Fid the 12th term. c. 17.2, 14.94, 12.63, 1.32,... Fid the 1th term. d..3,.3,.3,.3,...fid the 8th term. e., 1 6, 1 3, 1,... 2 Fid the 21st term. f. 2, 4, 8, 16,... Fid the 1th term.. Idicate whether each situatio could be represeted by a arithmetic sequece or a geometric sequece. Give the value of the commo differece, d, for each arithmetic sequece ad of the commo ratio, r, for each geometric sequece. a. Phil reted a apartmet for $8 a moth. Each time he reewed his lease over the ext 3 years, his ladlord raised the ret by $. b. Leora was hired as a first-year teacher at a aual salary of $3,. She received a aual salary icrease of % for each of the ext 4 years. c. A laboratory techicia observes that the umber of bacteria i a coloy doubles every 12 hours. d. The umber of studets erolled i a high school is decreasig at arate of 7 studets per year. 6. Write a recursive formula for the sequece graphed at right. Fid the 42d term. 1 4 CHAPTER 1 Discoverig Advaced Algebra More Practice Your Skills 24 Key Curriculum Press

2 Lesso 1.2 Modelig Growth ad Decay 1. Fid the commo ratio for each sequece. a. 42, 126, 378, 1134,... b. 19.2, 3.84,.768,.136,... c. 9, 99, 18.9, ,... d. 18, 18, 648, 388.8,... e. 11., 43.7, 166.6, ,... f. 37, 142., 4.1, 2.77, Idetify each sequece i Exercise 1 as growth or decay ad give the percet icrease or decrease for each. 3. Write a recursive formula for each sequece i Exercise 1 ad fid the 6th term. Use u 1 for the first term give. 4. Factor each expressio so that the variable appears oly oce. a. x.2x b. y.19y c. 2A.33A d. 3B.7B e f g h Fid the percet icrease or percet decrease i each situatio. (Roud to the earest teth of a percet.) Idetify each chage as a icrease or a decrease. a. The umber of studets attedig a high school grew from 126 to 18. b. A computer origially priced at $21 was put o sale for $18. c. Whe Melissa reewed her lease, her ret wet up from $78 to $81. d. After layig off 6 employees, a compay had 1266 employees left. e. The value of a car depreciated from $1,9 to $12,42. f. The populatio of a small tow chaged from 16,3 to 17, Match each recursive formula to a graph. a. u 1 3 b. u 1 3 (1.3) 1 where 2 (1.) 1 where 2 c. u where 2 A. B. C Discoverig Advaced Algebra More Practice Your Skills CHAPTER 1 24 Key Curriculum Press

3 Lesso 1.3 A First Look at Limits 1. For each sequece, fid the value of u 1, u 2, ad u 3.Idetify the type of sequece (arithmetic, geometric, or shifted geometric) ad tell whether it is icreasig or decreasig. a. u 2 b. u where where 1 c. u 48 d. u where where 1 e. u f. u 49 (1.8) 1 2 where 1 (1.7) 1 where 1 2. Solve. a. r.9r 3 b. s 2.7s c. t.82t d. v 4 v e. w.6w 2 f. z.12z Fid the log-ru value for each sequece. a. u 2 b. u where where 1 c. u 48 d. u where where 1 e. u 62 f. u 4 (1.2) 1 where 1 (1.) 1 where 1 g. u h. u 3 (1.8) 1 2 where 1 (1.7) 1 3 where 1 4. Write a recursive formula for each sequece. Use u for the first term give. a., 2, 36, 48.8,... b. 1, 16, 226, 298.6,... c., 36, 27.6, 22.6,... d. 4, 44,.4, 6.64,... e. 18, 144, 111.6, 82.44,... f. 2, 128, 67, 36,... g., 6, 83, 146,... h. 9, 67, 48.6, 33.88,... 6 CHAPTER 1 Discoverig Advaced Algebra More Practice Your Skills 24 Key Curriculum Press

4 Lesso 1.4 Graphig Sequeces 1. Write five ordered pairs that represet poits o the graph of each sequece. a. u 2 b. u where where 1 c. u = d. u where where 1 e. u 6 f. u where where 1 2. Idetify each graph as a represetatio of a arithmetic sequece, a geometric sequece, or a shifted geometric sequece. Use a iformed guess to write a recursive rule for each. a. b c. d Imagie the graphs of the sequeces geerated by these recursive formulas. Describe each graph usig exactly three of these terms: arithmetic, geometric, shifted geometric, liear, oliear, icreasig, decreasig. a. u b. u where where 1 c. u 3 d. u where 1 (1.1) 1 where 1 e. u. f. u where 1 (1.3) 1 1 where 1 Discoverig Advaced Algebra More Practice Your Skills CHAPTER Key Curriculum Press

5 Lesso 1. Loas ad Ivestmets 1. Assume that each of the sequeces below represets a fiacial situatio. Idicate whether each represets a loa or a ivestmet, ad give the pricipal ad the deposit or paymet amout. a. u 1 (1.4) 1 1 where 1 b. u where c. u where 1 d. u where For each fiacial situatio represeted by a sequece i Exercise 1, give the aual iterest rate ad the frequecy with which iterest is compouded. 3. Fid the first moth s iterest o each loa. a. $2, loa; 6% aual iterest rate b. $1,6 loa; 4.6% aual iterest rate c. $122,7 loa;.7% aual iterest rate d. $49,2 loa; 7.3% aual iterest rate 4. Write a recursive formula for each fiacial situatio. a. You ivest $, at %, compouded quarterly, ad deposit a additioal $4 every 3 moths. b. You take out a car loa for $12, at 7.%, compouded mothly, ad you make mothly paymets of $3. c. You take out a home mortgage for $144, at 6.2%, compouded mothly, ad make mothly paymets of $99. d. You eroll i a ivestmet pla through your job that deducts $22 from your mothly paycheck ad deposits it ito a accout with a aual iterest rate of 3.7%, compouded mothly. 8 CHAPTER 1 Discoverig Advaced Algebra More Practice Your Skills 24 Key Curriculum Press