Lesson 1.1 Recursively Defined Sequences

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1 Lesso 1.1 Recursively Defied Sequeces 1. Fid the commo differece, d, for each arithmetic sequece ad the commo ratio, r, for each geometric sequece. a. 1., 1.,.,,.,... b..62,.12,.2,... c. 1,.2,.4,.8, Write the first six terms of each sequece ad idetify each sequece as arithmetic or geometric. a. u 1 18 b. u where where 2 3. Write a recursive formula to geerate each sequece. The fid the idicated term. a. 17.2, 14.94, 12.63, 1.32,... Fid the 1th term. b. 2, 4, 8, 16,... Fid the 1th term. 4. 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 aual 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.. 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 21 Key Curriculum Press

2 Lesso 1.2 Modelig Growth ad Decay 1. Fid the commo ratio for each sequece ad idetify the sequece as growth or decay. Give the percet icrease or decrease for each. a. 42, 126, 378, 1134,... b. 19.2, 3.84,.768,.136,... c. 9, 99, 18.9, ,... d. 18, 18, 648, 388.8, Write a recursive formula for each sequece i Exercise 1. Use u for the first term give ad fid u. 3. Factor each expressio so that the variable appears oly oce. For example, x.x factors ito x (1.). a. y.19y b. 2A.33A c d Write a recursive formula for the sequece 3, 8., 26, 77.,..... Match each recursive formula to a graph. a. u 3 b. u 3 (1.3) 1 where 1 (1.) 1 where 1 c. u 3. 1 where 1 A. B. C Discoverig Advaced Algebra More Practice Your Skills CHAPTER 1 21 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 1 (1.8) 1 2 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 48 b. u where where 1 c. u 62 d. u 4 (1.2) 1 where 1 (1.) 1 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,... 6 CHAPTER 1 Discoverig Advaced Algebra More Practice Your Skills 21 Key Curriculum Press

4 Lesso 1.4 Graphig Sequeces 1. Write five ordered pairs that represet poits o the graph of each sequece. a. b 2 b. b 1 b b 1 8 where 1 b.1b 1 where 1 c. b d. b 1 b 2.b 1 1 where 1 b.8b 1 1 where 1 2. Match each formula with a graph ad idetify the sequece as arithmetic or geometric. a. u 1 b. u 3 c. u where 1 1 where where 1 A. B. C 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. t b. a 1 t t 1 1 where 1 a.7a 1 1 where 1 c. u 3 d. t where 1 t (1.1)t 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. a 1 a (1.4)a 1 1 where 1 b. a 13, a a 1 1 where 1 c. a 182 a a 1 12 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 4. Write a recursive formula for each fiacial situatio. a. You take out a home mortgage for $144, at 6.2%, compouded mothly, ad make mothly paymets of $99. b. 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 21 Key Curriculum Press