Upload
others
View
14
Download
0
Embed Size (px)
Citation preview
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∞?