Use the given information to write the first 5 terms of the sequence and the 20 th term. 6. a1= 4, d= 8 7. a1= 10, d= -6 8.

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1 Arithmetic Sequences Class Work Find the common difference in sequence, and then write the next 3 terms in the sequence. 1. 3, 7,11, 15, 2. 1, 8, 15, 22, 3. 5, 2, -1, -4, 4. 68, 56, 44, 32, , 2.6, 3.9, 5.2, Use the given information to write the first 5 terms of the sequence and the 20 th term. 6. a1= 4, d= 8 7. a1= 10, d= a2= 9, d= 6 9. a15= 32, d= , 7, 10, 13, Solve the following questions. 11. What is the common difference when a1=8 and a11=40? 12. What is 20 th term if a1=12 and a10= -33? 13. If a1=12, an=111,and d = 9, what is n? 14. Tom works at a car dealership selling cars. If he makes $4000 a month and $250 per car he sells, how much did he make in July if he sold 12 cars? In August he made $6500, how many cars did he sell? Find the missing term(s) in the sequence , _, , _, _, , _, _, , _, _, _, 68 Pre-Calc Sequences & Series ~1~ NJCTL.org

2 Arithmetic Sequences Homework Find the common difference in sequence, and then write the next 3 terms in the sequence , 11, 20, 29, , -6, 5, 16, , 9, 6, 3, , 31, 17, 3, , 5.7, 7.1, 8.5, Use the given information to write the first 5 terms of the sequence and the 20 th term. 24. a1= 4, d= a1= 10, d= a2= 9, d= a15= 32, d= , 5, 11, 17, Solve the following questions. 29. What is the common difference when a1=3 and a11=44? 30. What is 20 th term if a1=2 and a10= -34? 31. If a1=22, an=78,and d = 8, what is n? 32. Tom works at a car dealership selling cars. If he makes $4000 a month and $250 per car he sells, how much did he make in July if he sold 16 cars? In August he made $10,000, how many cars did he sell? Find the missing term(s) in the sequence , _, , _, _, , _, _, , _, _, _, 48 Pre-Calc Sequences & Series ~2~ NJCTL.org

3 Arithmetic Series Class Work Find the indicated Sn. 37. a1 = 5, a12 = 38, find S a1 = 8, a10 = 89, find S a1 = 12, a9 = -36, find S , 12, 20, 28, find S , 9, 6, 3, find S , find Sn 43. a1= 10, d= -3 find S9 Evaluate the following a=1 4a b 1 b= c=12 2c d + 1 d=8 Pre-Calc Sequences & Series ~3~ NJCTL.org

4 Arithmetic Series Homework Find the indicated Sn. 48. a1 = 2, a14 = -24, find S a1 = 18, a11 = 58, find S a1 = 15, a8 = -20, find S , 12, 18, 24, find S , 14, 10, 6, find S , find Sn 54. a1= 10, d= -2 find S12 Evaluate the following a=1 5a b 3 b= c=12 3c d + 1 d=8 Pre-Calc Sequences & Series ~4~ NJCTL.org

5 Geometric Sequences Class Work Find the common ratio in sequence, and then write the next 3 terms in the sequence , 10, 20, 40, 60. 4, -12, 36, -108, , -8, 4, -2, 62. 6, 9, 13.5, 20.25, Use the given information to write the first 4 terms of the sequence and the 10 th term. 63. a1=6 and r=3 64. a1=12 and r= a1=8 and r= a3=20 and r=2 67. A cell reproduces by splitting in half every half hour, how many cells will there be in 6 hours if a the start there were 10? Find the missing term(s) in the sequence , _, , _, _, , _, _, , _, _, _, 4375 Pre-Calc Sequences & Series ~5~ NJCTL.org

6 Geometric Sequences Homework Find the common ratio in sequence, and then write the next 3 terms in the sequence , 8, 32, 128, 73. 6, -12, 24, -48, , -10, 5, -2.5, , 5, -6.25, , Use the given information to write the first 4 terms of the sequence and the 10 th term. 76. a1=8 and r= a1=20 and r= a1=16 and r= a3=36 and r=3 80. A cell reproduces by splitting in half every 15 minutes, how many cells will there be in 5 hours if a the start there were 20? Find the missing term(s) in the sequence , _, , _, _, , _, _, , _, _, _, 1792 Pre-Calc Sequences & Series ~6~ NJCTL.org

7 Geometric Series Class Work Find the indicated Sn. 85. a1=7, r=3, and n= 8, find S8 86. a1=6, r= -2, and n= 12, find S a1=8, r=.5, and n= 6 find S6 88. a1=4 and a8 = , find S8 89. a1=4 and a8 = , find S6 Evaluate the following n=1 2 3 n n=1 3 2 n n=1 2 ( 2) n n=1 6 (.5) n 1 Pre-Calc Sequences & Series ~7~ NJCTL.org

8 Geometric Series Homework Find the indicated Sn. 94. a1=6, r=5, find S9 95. a1=10, r= -4, find S7 96. a1=48, r=.5, find S8 97. a1=12 and a8 = 26244, find S8 98. a1=12 and a8 = 26244, find S6 Evaluate the following n=1 6 3 n n=1 8 (4) n n=1 10 (1.5) n n=1 12 ( 2) n 1 Pre-Calc Sequences & Series ~8~ NJCTL.org

9 Infinite Geometric Series Class Work Find the sum of infinite sequence if one exists a1= 5 and r= 2 / a1= -4 and r=- 1 / a1= 6 and r= 5 / a2=8 and r=- 1 / ( 1 x=1 3 )n ( 5 x=1 4 )n ( 1 x=1 9 )n 1 Infinite Geometric Series Homework Find the sum of infinite sequence if one exists a1= 3 and r= 1 / a1= -6 and r=- 3 / a1= 7 and r= 3 / a2=12 and r=- 3 / ( 1 x= ( 5 x=1 6 )n ( 1 x=1 3 )n 1 2 )n 1 Pre-Calc Sequences & Series ~9~ NJCTL.org

10 Special Sequences Class Work Identify the sequence as arithmetic, geometric, or neither. Write the first 5 terms a1=3; an= 4an a1=6; an= -3an a1=-4; an= an a1=-7; an= 2an a1=8; an= an a1=1; an= 6an a1=-9;a2=6; an= 4an-1 + 2an a1=10; a2= 8; an= -1an-1 + 2an-2 Special Sequences Homework Identify the sequence as arithmetic, geometric, or neither. Write the first 5 terms a1=2; an= an a1=8; an= -2an a1=-14; an= an a1=-1; an= 6an a1=12; an= 3an a1=5; an=2 + 5an a1=-4;a2=3; an= 2an-1 + 3an a1=1; a2= 1; an= an-1 + an-2 Pre-Calc Sequences & Series ~10~ NJCTL.org

11 Binomial Theorem Class Work Consider the binomial expansion of (4x 2y) n to identify the term nd term when n= th term when n = th term when n= rd term when n= th term when n=9 Binomial Theorem Homework Consider the binomial expansion of (2a 4b) n to identify the term nd term when n= th term when n = th term when n= rd term when n= th term when n=10 Pre-Calc Sequences & Series ~11~ NJCTL.org

12 Sequences and Series Unit Review Multiple Choice 1. The sequence 2, 6, 10, 14, has a. a common ratio of 3 b. a common difference of 3 c. a common ratio of 4 d. a common difference of 4 2. The sequence 8, -4, 2, -1, has a. a common ratio of 1/2 b. a common difference of 1/2 c. a common ratio of -1/2 d. a common difference of -1/2 3. The next term in the sequence 7, 13, 19, 25 is a. 6 b. 31 c. 32 d The next term in the sequence 64, 48, 36, 27 is a. 20 b c d What is the common difference in this arithmetic sequence: 4,,,, 25 a b. 6.5 c. 7 d What is the common ratio in this geometric sequence: 4,,, 108 a. ±3 b. 3 c. ±27 d What is the common ratio in this geometric sequence: 32,,,, 2 a. ±.5 b..5 c. ±2 d a1 = 6 and d = 8 find S6 a. 46 b. 48 c. 108 d a1=8 and r = -4, find S6 a b c d. -12 Pre-Calc Sequences & Series ~12~ NJCTL.org

13 10. 8 n=4 3n = a. 24 b. 36 c. 72 d n 5 a. 45 b. 40 c. 28 d. 13 n=1 = ( 1 n=1 2 )n 1 a. 0 b. 2.5 c. 2 2 /3 d. not possible 13. Find the first 5 terms of a1 = 3 and an= 2an-1 a. 3, 6, 9, 12, 15 b. 3, 5, 7, 9, 11 c. 3, 6, 12, 24, 36 d. 3, 6, 12, 24, Find the first 5 terms of a1 = 2 and a2=8 and an= an-1 + an-2 a. 2, 8, 10, 18, 28 b. 2, 8, 10, 12, 20 c. 2, 8, 16, 32, 64 d. 2, 8, 16, 24, The sequence 1, 1, 2, 3, 5, 8, is a. arithmetic b. geometric c. Fibonacci d. None of the above 16. The coefficient of the 3 rd term of (2x 3y) 4 is a b. 216 c. -96 d. 96 Pre-Calc Sequences & Series ~13~ NJCTL.org

14 Extended Response 1. Your rich uncle wants to hire you to work for his company for 30 days. He offers to pay you (A) $1000 per day or (B) 1 cent the first day and double the pay each day thereafter. a. How much money do you make in 30 days of pay A? b. How much do you make on day 30 of pay B? c. How much money do you make in 30 days of pay B? 2. Given the sequence 2,,, -16 a. What are the missing terms if the sequence were geometric? b. What are the missing terms if the sequence were arithmetic? c. What is the sum of each sequence from part a and b. Use Sigma notation. Pre-Calc Sequences & Series ~14~ NJCTL.org

15 3. Given the arithmetic sequence of 4, 10, 16, 22, a. What is a20? b. What is an? c. What is S20? d. What is Sn? 4. Given the geometric sequence of 20, -10, 5, -2.5, a. What is a10? b. What is an? c. What is S10? d. What is Sn? e. What is S? Pre-Calc Sequences & Series ~15~ NJCTL.org

Section 8.1. Sequences and Series

Section 8.1. Sequences and Series Section 8.1 Sequences and Series Sequences Definition A sequence is a list of numbers. Definition A sequence is a list of numbers. A sequence could be finite, such as: 1, 2, 3, 4 Definition A sequence