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, …
  1. 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.

  1. a1= 4, d= 87. a1= 10, d= -68. a2=9, d= 6
  1. a15= 32, d= 510. 4, 7, 10, 13, …

Solve the following questions.

  1. What is the common difference when a1=8 and a11=40?
  2. What is 20th term if a1=12 and a10= -33?13. If a1=12, an=111 ,and d = 9, what is n?
  1. 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.

  1. 3, _ , 916. 4, _ , _ , 19
  1. 5, _ , _ , -718. 20, _ , _ , _, 68

Arithmetic Sequences – Homework

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

  1. 2, 11, 20, 29, …20. -17, -6, 5,16, …21. 12, 9, 6, 3, …
  1. 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.

  1. a1= 4, d= 325. a1= 10, d= -826. a2= 9, d= 14
  1. a15= 32, d= 728. -1, 5, 11, 17, …

Solve the following questions.

  1. What is the common difference when a1=3 and a11=44?
  2. What is 20th term if a1=2 and a10= -34?31. If a1=22, an=78 ,and d = 8, what is n?
  1. 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.

  1. 4, _ , 1634. 3, _ , _ , 27
  1. 12, _ , _ , -936. 12, _ , _ , _, 48

Arithmetic Series – Class Work

Find the indicated Sn.

  1. a1 = 5, a12 = 38, find S1238. a1 = 8, a10 = 89, find S10
  1. a1 = 12, a9 = -36, find S940. 4, 12, 20, 28, … find S8
  1. 12, 9, 6, 3, … find S1242. 15 + 18 + 21 + … +63, find Sn
  1. a1= 10 , d= -3 find S9

Evaluate the following

  1. 45.
  1. 47.


Arithmetic Series – Homework

Find the indicated Sn.

  1. a1 = 2, a14 = -24, find S1449. a1 = 18, a11 = 58, find S11
  1. a1 = 15, a8 = -20, find S851. 6, 12, 18, 24, … find S13
  1. 18, 14, 10, 6, … find S1153. 22 + 29 + 36 + … + 85, find Sn
  1. a1= 10 , d= -2 find S12

Evaluate the following

  1. 56.
  1. 58.

Geometric Sequences – Class Work

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

  1. 5, 10, 20, 40, …60. 4, -12, 36, -108, …
  1. 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.

  1. a1=6 and r=364. a1=12 and r=.5
  1. a1=8 and r= 466. a3=20 and r=2
  1. 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?

Find the missing term(s) in the sequence.

  1. 4, _ , 14469. 5, _ , _, 135
  1. 6, _ , _, -.7571. 7, _ , _ , _ , 4375

Geometric Sequences – Homework

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

  1. 2, 8, 32,128, …73. 6, -12, 24, -48, …
  1. 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.

  1. a1=8 and r=1077. a1=20 and r=.5
  1. a1=16 and r= -279. a3=36 and r=3
  1. 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?

Find the missing term(s) in the sequence.

  1. 4, _ , 3682. 5, _ , _, 1080
  1. 6, _ , _, 307284. 7, _ , _ , _ , 1792

Geometric Series – Class Work

Find the indicated Sn.

  1. a1=7, r=3, and n= 8, find S886. a1=6, r= -2, and n= 12, find S12
  1. a1=8, r=.5, and n= 6 find S688. a1=4 and a8 = 312500, find S8
  1. a1=4 and a8 = 312500, find S6

Evaluate the following

  1. 91.
  1. 93.


Geometric Series – Homework

Find the indicated Sn.

  1. a1=6, r=5, find S995. a1=10, r= -4, find S7
  1. a1=48, r=.5, find S897. a1=12 and a8 = 26244, find S8
  1. a1=12 and a8 = 26244, find S6

Evaluate the following

  1. 100.
  1. 102.

Infinite Geometric Series – Class Work

Find the sum of the infinite series if one exists.

  1. a1= 5 and r= 2/3104. a1= -4 and r=-1/2105. a1= 6 and r=5/4
  1. a2=8 and r=-1/4107. 32 + 24 + 18 + 13.5+…108. 12 + 10 + + + …
  1. 110. 111.


Infinite Geometric Series – Homework

Find the sum of the infinite series if one exists.

  1. a1= 3 and r= 1/2113. a1= -6 and r=-3/2114. a1= 7 and r=3/7
  1. a2=12 and r=-3/5116. 40 + 30 + 22.5 + 16.875+…117. 5 – 6 + – + …
  1. 119. 120.

Special Sequences – Class Work

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

  1. a1=3; an= 4an-1 + 2122. a1=6; an= -3an-1123. a1=-4; an= an-1 + 8
  1. a1=-7; an= 2an-1 -1125. a1=8; an= an-1 + 2126. a1=1; an= 6an-1
  1. a1=-9;a2=6; an= 4an-1 + 2an-2128. 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.

  1. a1=2; an= an-1 + 8130. a1=8; an= -2an-1131. a1=-14; an= an-1– 5
  1. a1=-1; an= 6an-1133. a1=12; an= 3an-1134. a1=5; an=2 + 5an-1
  1. a1=-4;a2=3; an= 2an-1 + 3an-2136. a1=1; a2= 1; an= an-1 + an-2

Binomial Theorem – Class Work

Consider the binomial expansion of to identify the term.

  1. 2nd term when n=3138. 4th term when n =5
  1. 7th term when n=8140. 3rd term when n=3
  1. 6th term when n=9

Binomial Theorem – Homework

Consider the binomial expansion of to identify the term.

  1. 2nd term when n=4143. 4th term when n =6
  1. 7th term when n=7145. 3rd term when n=2
  1. 6th term when n=10

Sequences and Series Unit Review
Multiple Choice

  1. The sequence 2, 6, 10, 14,… has
  2. a common ratio of 3
  3. a common difference of 3
  4. a common ratio of 4
  5. a common difference of 4
  6. The sequence 8, -4, 2, -1 ,… has
  7. a common ratio of 1/2
  8. a common difference of 1/2
  9. a common ratio of -1/2
  10. a common difference of -1/2
  11. The next term in the sequence 7, 13, 19, 25 is
  12. 6
  13. 31
  14. 32
  15. 48
  16. The next term in the sequence 64, 48, 36, 27 is
  17. 20
  18. 20.25
  19. 20.5
  20. 21
  21. What is the common difference in this arithmetic sequence: 4, __, __,__, 25
  22. 5.25
  23. 6.5
  24. 7
  25. 7.4
  26. What is the common ratio in this geometric sequence: 4, __, __, 108
  27. 3
  28. 27
  29. What is the common ratio in this geometric sequence: 32, __, __, __, 2
  30. .5
  31. 2
  32. a1 = 6 and d = 8 find S6
  33. 46
  34. 48
  35. 108
  36. 156
  37. a1=8 and r = -4, find S6
  38. -10920
  39. -8192
  40. -6552
  41. -12
  42. 24
  43. 36
  44. 72
  45. 90
  46. =
  47. 45
  48. 40
  49. 28
  50. 13
  51. 0
  52. 2.5
  53. 2 2/3
  54. not possible
  55. Find the first 5 terms of a1 = 3 and an= 2an-1
  56. 3, 6, 9, 12, 15
  57. 3, 5, 7, 9, 11
  58. 3, 6, 12, 24, 36
  59. 3, 6, 12, 24, 48
  60. Find the first 5 terms of a1 = 2 and a2=8 and an= an-1 + an-2
  61. 2, 8, 10, 18, 28
  62. 2, 8, 10, 12, 20
  63. 2, 8, 16, 32, 64
  64. 2, 8, 16, 24, 32
  65. The sequence 1, 1, 2, 3, 5, 8, … is
  66. arithmetic
  67. geometric
  68. Fibonacci
  69. None of the above
  70. The coefficient of the 3rd term of (2x – 3y)4 is
  71. -216
  72. 216
  73. -96
  74. 96

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.
  2. How much money do you make in 30 days of pay A?
  3. How much do you make on day 30 of pay B?
  4. How much money do you make in 30 days of pay B?
  5. Given the sequence 2, ___, ___, -16
  6. What are the missing terms if the sequence were geometric?
  7. What are the missing terms if the sequence were arithmetic?
  8. What is the sum of each sequence from part a and b. Use Sigma notation.
  9. Given the arithmetic sequence of 4, 10, 16, 22, …
  10. What is a20?
  11. What is an?
  12. What is S20?
  13. What is Sn?
  14. Given the geometric sequence of 20, -10, 5, -2.5, …
  15. What is a10?
  16. What is an?
  17. What is S10?
  18. What is Sn?
  19. What is ?

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