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Pre-Calc Sequences & Series ~1~ NJCTL.org 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, … 5. 1.3, 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= -6 8. a2= 9, d= 6 9. a15= 32 , d= 5 10. 4, 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. 15. 3, _ , 9 16. 4, _ , _ , 19 17. 5, _ , _ , -7 18. 20, _ , _ , _, 68

# Arithmetic Sequences Class Work - NJCTLcontent.njctl.org/courses/math/pre-calculus/sequences... · 2014-11-11 · Pre-Calc Sequences & Series ~12~ NJCTL.org Sequences and Series Unit

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Pre-Calc Sequences & Series ~1~ NJCTL.org

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, … 5. 1.3, 2.6, 3.9, 5.2, …

Use the given information to write the first 5 terms of the sequence and the 20th term.

6. a1= 4, d= 8 7. a1= 10, d= -6 8. a2= 9, d= 6

9. a15= 32 , d= 5 10. 4, 7, 10, 13, …

Solve the following questions.

11. What is the common difference when a1=8 and a11=40?

12. What is 20th 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.

15. 3, _ , 9 16. 4, _ , _ , 19

17. 5, _ , _ , -7 18. 20, _ , _ , _, 68

Pre-Calc Sequences & Series ~2~ NJCTL.org

Arithmetic Sequences – Homework

Find the common difference in sequence, and then write the next 3 terms in the sequence.

19. 2, 11, 20, 29, … 20. -17, -6, 5, 16, … 21. 12, 9, 6, 3, …

22. 45, 31, 17, 3, … 23. 4.3, 5.7, 7.1, 8.5, …

Use the given information to write the first 5 terms of the sequence and the 20th term.

24. a1= 4, d= 3 25. a1= 10, d= -8 26. a2= 9, d= 14

27. a15= 32 , d= 7 28. -1, 5, 11, 17, …

Solve the following questions.

29. What is the common difference when a1=3 and a11=44?

30. What is 20th 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.

33. 4, _ , 16 34. 3, _ , _ , 27

35. 12, _ , _ , -9 36. 12, _ , _ , _, 48

Pre-Calc Sequences & Series ~3~ NJCTL.org

Arithmetic Series – Class Work

Find the indicated Sn.

37. a1 = 5, a12 = 38, find S12 38. a1 = 8, a10 = 89, find S10

39. a1 = 12, a9 = -36, find S9 40. 4, 12, 20, 28, … find S8

41. 12, 9, 6, 3, … find S12 42. 15 + 18 + 21 + … + 63, find Sn

43. a1= 10 , d= -3 find S9

Evaluate the following

44. ∑ 4𝑎5𝑎=1 45. ∑ 2𝑏 − 18

𝑏=3

46. ∑ −2𝑐15𝑐=12 47. ∑ 3𝑑 + 122

𝑑=8

Pre-Calc Sequences & Series ~4~ NJCTL.org

Arithmetic Series – Homework

Find the indicated Sn.

48. a1 = 2, a14 = -24, find S14 49. a1 = 18, a11 = 58, find S11

50. a1 = 15, a8 = -20, find S8 51. 6, 12, 18, 24, … find S13

52. 18, 14, 10, 6, … find S11 53. 22 + 29 + 36 + … + 85, find Sn

54. a1= 10 , d= -2 find S12

Evaluate the following

55. ∑ 5𝑎5𝑎=1 56. ∑ 2𝑏 − 38

𝑏=3

57. ∑ −3𝑐15𝑐=12 58. ∑ 4𝑑 + 122

𝑑=8

Pre-Calc Sequences & Series ~5~ NJCTL.org

Geometric Sequences – Class Work

Find the common ratio in sequence, and then write the next 3 terms in the sequence.

59. 5, 10, 20, 40, … 60. 4, -12, 36, -108, …

61. 16, -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 10th term.

63. a1=6 and r=3 64. a1=12 and r=.5

65. a1=8 and r= 4 66. 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.

68. 4, _ , 144 69. 5, _ , _, 135

70. 6, _ , _, -.75 71. 7, _ , _ , _ , 4375

Pre-Calc Sequences & Series ~6~ NJCTL.org

Geometric Sequences – Homework

Find the common ratio in sequence, and then write the next 3 terms in the sequence.

72. 2, 8, 32, 128, … 73. 6, -12, 24, -48, …

74. 20, -10, 5, -2.5, … 75. -4, 5, -6.25, 7.8125 , …

Use the given information to write the first 4 terms of the sequence and the 10th term.

76. a1=8 and r=10 77. a1=20 and r=.5

78. a1=16 and r= -2 79. 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.

81. 4, _ , 36 82. 5, _ , _, 1080

83. 6, _ , _, 3072 84. 7, _ , _ , _ , 1792

Pre-Calc Sequences & Series ~7~ NJCTL.org

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 S12

87. a1=8, r=.5, and n= 6 find S6 88. a1=4 and a8 = 312500, find S8

89. a1=4 and a8 = 312500, find S6

Evaluate the following

90. ∑ 2 ∙ 3𝑛−14𝑛=1 91. ∑ 3 ∙ 2𝑛−15

𝑛=1

92. ∑ −2 ∙ (−2)𝑛−16𝑛=1 93. ∑ 6 ∙ (−.5)𝑛−15

𝑛=1

Pre-Calc Sequences & Series ~8~ NJCTL.org

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

99. ∑ 6 ∙ 3𝑛−14𝑛=1 100. ∑ 8 ∙ (4)𝑛−16

𝑛=1

101. ∑ −10 ∙ (1.5)𝑛−17𝑛=1 102. ∑ 12 ∙ (−2)𝑛−18

𝑛=1

Pre-Calc Sequences & Series ~9~ NJCTL.org

Infinite Geometric Series – Class Work

Find the sum of infinite sequence if one exists.

103. a1= 5 and r= 2/3 104. a1= -4 and r=-1/2 105. a1= 6 and r=5/4

106. a2=8 and r=-1/4 107. 32 + 24 + 18 + 13.5+… 108. 12 + 10 + 25

3 +

125

18 + …

109. ∑ 3 (1

3)

n−1∞x=1 110. ∑ −2 (

5

4)

n−1∞x=1 111. ∑ 6 (

−1

9)

n−1∞x=1

Infinite Geometric Series – Homework

Find the sum of infinite sequence if one exists.

112. a1= 3 and r= 1/2 113. a1= -6 and r=-3/2 114. a1= 7 and r=3/7

115. a2=12 and r=-3/5 116. 40 + 30 + 22.5 + 16.875+… 117. 5 – 6 + 36

5 –

216

25 + …

118. ∑ 4 (−1

3)

n−1∞x=1 119. ∑ −8 (

5

6)

n−1∞x=1 120. ∑ 12 (

−1

2)

n−1∞x=1

Pre-Calc Sequences & Series ~10~ NJCTL.org

Special Sequences – Class Work

Identify the sequence as arithmetic, geometric, or neither. Write the first 5 terms.

121. a1=3; an= 4an-1 + 2 122. a1=6; an= -3an-1 123. a1=-4; an= an-1 + 8

124. a1=-7; an= 2an-1 -1 125. a1=8; an= an-1 + 2 126. a1=1; an= 6an-1

127. a1=-9;a2=6; an= 4an-1 + 2an-2 128. 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.

129. a1=2; an= an-1 + 8 130. a1=8; an= -2an-1 131. a1=-14; an= an-1 – 5

132. a1=-1; an= 6an-1 133. a1=12; an= 3an-1 134. a1=5; an=2 + 5an-1

135. a1=-4;a2=3; an= 2an-1 + 3an-2 136. a1=1; a2= 1; an= an-1 + an-2

Pre-Calc Sequences & Series ~11~ NJCTL.org

Binomial Theorem – Class Work

Consider the binomial expansion of (4𝑥 − 2𝑦)𝑛 to identify the term.

137. 2nd term when n=3 138. 4th term when n =5

139. 7th term when n=8 140. 3rd term when n=3

141. 6th term when n=9

Binomial Theorem – Homework

Consider the binomial expansion of (2𝑎 − 4𝑏)𝑛 to identify the term.

142. 2nd term when n=4 143. 4th term when n =6

144. 7th term when n=7 145. 3rd term when n=2

146. 6th term when n=10

Pre-Calc Sequences & Series ~12~ NJCTL.org

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. 48

4. The next term in the sequence 64, 48, 36, 27 is

a. 20

b. 20.25

c. 20.5

d. 21

5. What is the common difference in this arithmetic sequence: 4, __, __,__, 25

a. 5.25

b. 6.5

c. 7

d. 7.4

6. What is the common ratio in this geometric sequence: 4, __, __, 108

a. ±3

b. 3

c. ±27

d. 27

7. What is the common ratio in this geometric sequence: 32, __, __, __, 2

a. ±.5

b. .5

c. ±2

d. 2

8. a1 = 6 and d = 8 find S6

a. 46

b. 48

c. 108

d. 156

9. a1=8 and r = -4, find S6

a. -10920

b. -8192

c. -6552

d. -12

Pre-Calc Sequences & Series ~13~ NJCTL.org

10. ∑ 3n =8n=4

a. 24

b. 36

c. 72

d. 90

11. ∑ 2n − 59n=1 =

a. 45

b. 40

c. 28

d. 13

12. ∑ 4 (−1

2)

𝑛−1∞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, 48

14. 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, 32

15. 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 3rd term of (2x – 3y)4 is

a. -216

b. 216

c. -96

d. 96

Pre-Calc Sequences & Series ~14~ NJCTL.org

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 ~15~ NJCTL.org

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∞?