arithmetic sequences class work -...

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

Arithmetic Sequences – Class Work

Find the common difference in the 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

𝒅 = 𝟒

𝟏𝟗, 𝟐𝟑, 𝟐𝟕

𝒅 = 𝟕

𝟐𝟗, 𝟑𝟔, 𝟒𝟑

𝒅 = −𝟑

−𝟕, −𝟏𝟎, −𝟏𝟑

𝒅 = −𝟏𝟐

𝟐𝟎, 𝟖, −𝟒

𝒅 = 𝟏. 𝟑

𝟔. 𝟓, 𝟕. 𝟖, 𝟗. 𝟏

𝟒, 𝟏𝟐, 𝟐𝟎, 𝟐𝟖, 𝟑𝟔

𝒂𝟐𝟎 = 𝟏𝟓𝟔

𝟏𝟎, 𝟒, −𝟐, −𝟖, −𝟏𝟒

𝒂𝟐𝟎 = −𝟏𝟎𝟒

𝟑, 𝟗, 𝟏𝟓, 𝟐𝟏, 𝟐𝟕

𝒂𝟐𝟎 = 𝟏𝟏𝟕

−𝟑𝟖, −𝟑𝟑, −𝟐𝟖, − 𝟐𝟑, −𝟏𝟖

𝒂𝟐𝟎 = 𝟓𝟕

𝟒, 𝟕, 𝟏𝟎, 𝟏𝟑, 𝟏𝟔

𝒂𝟐𝟎 = 𝟔𝟏

𝒅 = 𝟑. 𝟐

𝒂𝟐𝟎 = −𝟖𝟑 𝒏 = 𝟏𝟐

$𝟕𝟎𝟎𝟎; 𝟏𝟎 𝒄𝒂𝒓𝒔

𝟔

𝟏, −𝟑

𝟗, 𝟏𝟒

𝟑𝟐, 𝟒𝟒, 𝟓𝟔


Arithmetic Sequences – Homework

Find the common difference in the 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, …


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?


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

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

𝒅 = 𝟗

𝟑𝟖, 𝟒𝟕, 𝟓𝟔

𝒅 = 𝟏𝟏

𝟐𝟕, 𝟑𝟖, 𝟒𝟗

𝒅 = −𝟑

𝟎, −𝟑, −𝟔

𝒅 = −𝟏𝟒

−𝟏𝟏, −𝟐𝟓, −𝟑𝟗

𝒅 = 𝟏. 𝟒

𝟗. 𝟗, 𝟏𝟏. 𝟑, 𝟏𝟐. 𝟕

𝟒, 𝟕, 𝟏𝟎, 𝟏𝟑, 𝟏𝟔

𝒂𝟐𝟎 = 𝟔𝟏

𝟏𝟎, 𝟐, −𝟔, −𝟏𝟒, −𝟐𝟐

𝒂𝟐𝟎 = −𝟏𝟒𝟐

−𝟓, 𝟗, 𝟐𝟑, 𝟑𝟕, 𝟓𝟏

𝒂𝟐𝟎 = 𝟐𝟔𝟏

−𝟔𝟔, −𝟓𝟗, −𝟓𝟐, −𝟒𝟓, −𝟑𝟖

𝒂𝟐𝟎 = 𝟔𝟕

−𝟏, 𝟓, 𝟏𝟏, 𝟏𝟕, 𝟐𝟑

𝒂𝟐𝟎 = 𝟏𝟏𝟑

𝒅 = 𝟒. 𝟏

𝒂𝟐𝟎 = −𝟕𝟒 𝒏 = 𝟖

$𝟖𝟎𝟎𝟎; 𝟐𝟒 𝒄𝒂𝒓𝒔

𝟏𝟎

𝟓, −𝟐

𝟏𝟏, 𝟏𝟗

𝟐𝟏, 𝟑𝟎, 𝟑𝟗


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

𝑺𝟏𝟐 = 𝟐𝟓𝟖 𝑺𝟏𝟎 = 𝟒𝟖𝟓

𝑺𝟗 = −𝟏𝟎𝟖 𝑺𝟖 = 𝟐𝟓𝟔

𝑺𝟏𝟐 = −𝟓𝟒 𝑺𝒏 = 𝟔𝟔𝟑

𝑺𝟗 = −𝟏𝟖

𝟔𝟎 𝟔𝟎

−𝟏𝟎𝟖 𝟔𝟗𝟎


Arithmetic Series – Homework


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


55. ∑ 5𝑎5𝑎=1 56. ∑ 2𝑏 − 38

𝑏=3

57. ∑ −3𝑐15𝑐=12 58. ∑ 4𝑑 + 122

𝑑=8

𝑺𝟏𝟒 = −𝟏𝟓𝟒 𝑺𝟏𝟏 = 𝟒𝟏𝟖

𝑺𝟖 = −𝟐𝟎 𝑺𝟏𝟑 = 𝟓𝟒𝟔

𝑺𝟏𝟏 = −𝟐𝟐

𝑺𝟏𝟐 = −𝟏𝟐

𝑺𝒏 = 𝟓𝟑𝟓

𝟕𝟓

−𝟏𝟔𝟐

𝟒𝟖

𝟗𝟏𝟓


Geometric Sequences – Class Work

Find the common ratio in the 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, …


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 at the

start there were 10?


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

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

𝒓 = 𝟐

𝟖𝟎, 𝟏𝟔𝟎, 𝟑𝟐𝟎

𝒓 = −𝟑

𝟑𝟐𝟒, −𝟗𝟕𝟐, 𝟐𝟗𝟏𝟔

𝒓 = −𝟏

𝟐

𝟏, −𝟏

𝟐,

𝟏

𝟒

𝒓 = 𝟏. 𝟓

𝟑𝟎. 𝟑𝟕𝟓, 𝟒𝟓. 𝟓𝟔𝟐𝟓, 𝟔𝟖. 𝟑𝟒𝟑𝟕𝟓

𝟔, 𝟏𝟖, 𝟓𝟒, 𝟏𝟔𝟐

𝒂𝟏𝟎 = 𝟏𝟏𝟖𝟎𝟗𝟖

𝟏𝟐, 𝟔, 𝟑, 𝟏. 𝟓

𝒂𝟏𝟎 = 𝟎. 𝟎𝟐𝟑𝟒𝟑𝟕𝟓

𝟖, 𝟑𝟐, 𝟏𝟐𝟖, 𝟓𝟏𝟐

𝒂𝟏𝟎 = 𝟐𝟎𝟗𝟕𝟏𝟓𝟐

𝟓, 𝟏𝟎, 𝟐𝟎, 𝟒𝟎

𝒂𝟏𝟎 = 𝟐𝟓𝟔𝟎

𝒂𝟏𝟐 = 𝟐𝟎, 𝟒𝟖𝟎 𝒄𝒆𝒍𝒍𝒔

𝟐𝟒 𝒐𝒓 − 𝟐𝟒 𝟏𝟓, 𝟒𝟓

−𝟑, 𝟏. 𝟓 𝟑𝟓, 𝟏𝟕𝟓, 𝟖𝟕𝟓

or

−𝟑𝟓, 𝟏𝟕𝟓, −𝟖𝟕𝟓


Geometric Sequences – Homework

Find the common ratio in the 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 , …


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 at

the start there were 20?


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

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

𝒓 = 𝟒

𝟓𝟏𝟐, 𝟐𝟎𝟒𝟖, 𝟖𝟏𝟗𝟐

𝒓 = −𝟐

𝟗𝟔, −𝟏𝟗𝟐, 𝟑𝟖𝟒

𝒓 = −𝟏

𝟐

𝟏. 𝟐𝟓, −𝟎. 𝟔𝟐𝟓, 𝟎. 𝟑𝟏𝟐𝟓

𝒓 = −𝟏. 𝟐𝟓

−𝟗. 𝟕𝟔𝟓𝟔𝟐𝟓, 𝟏𝟐. 𝟐𝟎𝟕𝟎𝟑𝟏𝟐𝟓, −𝟏𝟓. 𝟐𝟓𝟖𝟕𝟖𝟗𝟎𝟔

𝟖, 𝟖𝟎, 𝟖𝟎𝟎, 𝟖𝟎𝟎𝟎

𝒂𝟏𝟎 = 𝟖𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎𝟎

𝟐𝟎, 𝟏𝟎, 𝟓, 𝟐. 𝟓

𝒂𝟏𝟎 = 𝟎. 𝟎𝟑𝟗𝟎𝟔𝟐𝟓

𝟏𝟔, −𝟑𝟐, 𝟔𝟒, −𝟏𝟐𝟖

𝒂𝟏𝟎 = −𝟖𝟏𝟗𝟐

𝟒, 𝟏𝟐, 𝟑𝟔, 𝟏𝟎𝟖

𝒂𝟏𝟎 = 𝟕𝟖𝟕𝟑𝟐

𝒂𝟐𝟎 = 𝟐𝟎, 𝟗𝟕𝟏, 𝟓𝟐𝟎 𝒄𝒆𝒍𝒍𝒔

𝟏𝟐 𝒐𝒓 − 𝟏𝟐 𝟑𝟎, 𝟏𝟖𝟎

𝟒𝟖, 𝟑𝟖𝟒 𝟐𝟖, 𝟏𝟏𝟐, 𝟒𝟒𝟖

or

−𝟐𝟖, 𝟏𝟏𝟐, −𝟒𝟒𝟖


Geometric Series – Class Work


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


90. ∑ 2 ∙ 3𝑛−14𝑛=1 91. ∑ 3 ∙ 2𝑛−15

𝑛=1

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

𝑛=1

𝑺𝟖 = 𝟐𝟐𝟗𝟔𝟎 𝑺𝟏𝟐 = −𝟖𝟏𝟗𝟎

𝑺𝟔 = 𝟏𝟓. 𝟕𝟓 𝑺𝟖 = 𝟑𝟗𝟎𝟔𝟐𝟒

𝑺𝟔 = 𝟏𝟓𝟔𝟐𝟒

𝟖𝟎 𝟗𝟑

𝟒𝟐 𝟒. 𝟏𝟐𝟓


Geometric Series – Homework


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


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

𝑺𝟗 = 𝟐𝟗𝟐𝟗𝟔𝟖𝟔 𝑺𝟕 = 𝟑𝟐𝟕𝟕𝟎

𝑺𝟖 = 𝟗𝟓. 𝟔𝟐𝟓 𝑺𝟖 = 𝟑𝟗𝟑𝟔𝟎

𝑺𝟔 = 𝟒𝟑𝟔𝟖

𝟐𝟒𝟎 𝟏𝟎𝟗𝟐𝟎

−𝟑𝟐𝟏. 𝟕𝟏𝟖𝟕𝟓 −𝟏𝟎𝟐𝟎


Infinite Geometric Series – Class Work

Find the sum of the infinite series 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 the infinite series 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

𝟏𝟓 −𝟖

𝟑 𝒏𝒐𝒕 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆

−𝟏𝟐𝟖

𝟓= −𝟐𝟓. 𝟔 𝟏𝟐𝟖 𝟕𝟐

𝟗

𝟐= 𝟒. 𝟓 𝒏𝒐𝒕 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝟐𝟕

𝟒= 𝟓. 𝟒

𝟔 𝒏𝒐𝒕 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝟒𝟗

𝟒= 𝟏𝟐. 𝟐𝟓

−𝟐𝟓

𝟐= −𝟏𝟐. 𝟓 𝟏𝟔𝟎 𝒏𝒐𝒕 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆

𝟑 −𝟒𝟖 𝟖


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

𝑵𝒆𝒊𝒕𝒉𝒆𝒓

𝟑, 𝟏𝟒, 𝟓𝟖, 𝟐𝟑𝟒, 𝟗𝟑𝟖

𝑮𝒆𝒐𝒎𝒆𝒕𝒓𝒊𝒄

𝟔, −𝟏𝟖, 𝟓𝟒, −𝟏𝟔𝟐, 𝟒𝟖𝟔

𝑨𝒓𝒊𝒕𝒉𝒎𝒆𝒕𝒊𝒄

−𝟒, 𝟒, 𝟏𝟐, 𝟐𝟎, 𝟐𝟖


−𝟕, −𝟏𝟓, −𝟑𝟏, −𝟔𝟑, −𝟏𝟐𝟕


𝟖, 𝟏𝟎, 𝟏𝟐, 𝟏𝟒, 𝟏𝟔


𝟏, 𝟔, 𝟑𝟔, 𝟐𝟏𝟔, 𝟏𝟐𝟗𝟔


−𝟗, 𝟔, 𝟔, 𝟑𝟔, 𝟏𝟓𝟔


𝟏𝟎, 𝟖, 𝟏𝟐, 𝟒, 𝟐𝟎


𝟐, 𝟏𝟎, 𝟏𝟖, 𝟐𝟔, 𝟑𝟒


𝟖, −𝟏𝟔, 𝟑𝟐, −𝟔𝟒, 𝟏𝟐𝟖


−𝟏𝟒, −𝟏𝟗, −𝟐𝟒, −𝟐𝟗, −𝟑𝟒


−𝟏, −𝟔, −𝟑𝟔, −𝟐𝟏𝟔, −𝟏𝟐𝟗𝟔


𝟏𝟐, 𝟑𝟔, 𝟏𝟎𝟖, 𝟑𝟐𝟒, 𝟗𝟕𝟐


𝟓, 𝟐𝟕, 𝟏𝟑𝟕, 𝟔𝟖𝟕, 𝟑𝟒𝟑𝟕


−𝟒, 𝟑, −𝟔, −𝟑, −𝟐𝟒


𝟏, 𝟏, 𝟐, 𝟑, 𝟓


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

−𝟗𝟔𝒙𝟐𝒚 −𝟏𝟐𝟖𝟎𝒙𝟐𝒚𝟑

𝟐𝟖𝟔𝟕𝟐𝒙𝟐𝒚𝟔 𝟒𝟖𝒙𝒚𝟐

−𝟏𝟎𝟑𝟐𝟏𝟗𝟐𝒙𝟒𝒚𝟓

−𝟏𝟐𝟖𝒂𝟑𝒃 −𝟏𝟎𝟐𝟒𝟎𝒂𝟑𝒃𝟑

𝟓𝟕𝟑𝟒𝟒𝒂𝒃𝟔 𝟏𝟔𝒃𝟐

−𝟖𝟐𝟓𝟕𝟓𝟑𝟔𝒂𝟓𝒃𝟓


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

D

C

B

B

A

B

A

D

C


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

D

A

C

D

A

C

B


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.

$30,000

$5,368,709.12

$10,737,418.23

−𝟒, 𝟖

−𝟒, −𝟏𝟎

∑ 𝟐(−𝟐)𝒏−𝟏𝟒𝒏=𝟏 = −𝟏𝟎

∑ 𝟖 − 𝟔𝒏𝟒𝒏=𝟏 = −𝟐𝟖


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∞?

𝒂𝟐𝟎 = 𝟏𝟏𝟖

𝒂𝒏 = −𝟐 + 𝟔𝒏

𝑺𝟐𝟎 = 𝟏𝟐𝟐𝟎

𝑺𝒏 =𝒏

𝟐(𝟐 + 𝟔𝒏)

𝒂𝟏𝟎 = −𝟓

𝟏𝟐𝟖= −𝟎. 𝟎𝟑𝟗𝟎𝟔𝟐𝟓

𝒂𝒏 = 𝟐𝟎(−𝟏

𝟐)𝒏−𝟏

𝑺𝟏𝟎 =𝟏𝟕𝟎𝟓

𝟏𝟐𝟖= 𝟏𝟑. 𝟑𝟐𝟎𝟑𝟏𝟐𝟓

𝑺𝒏 =𝟒𝟎

𝟑(𝟏 − (−

𝟏

𝟐)𝒏)

𝑺∞ =𝟒𝟎

𝟑= 𝟏𝟑. �̅�

arithmetic sequences class work -...

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