Sequences

Arithmetic and geometric sequences from both ends — the nth term from the rule, and the rule from the terms.

4 sheets · 40 questions · one answer key · 5 pages

Recommended for grades 8–9

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Arithmetic: nth term Sheet 1 of 4

Arithmetic and geometric sequencesThe nth term of an arithmetic sequence

Name: Date:

Find the term shown for each sequence.

16, −1, −8, −15, …a₂₅ =

20, 3, 6, 9, …a₂₅ =

39, 13, 17, 21, …a₁₉ =

412, 16, 20, 24, …a₁₅ =

5−7, −9, −11, −13, …a₂₃ =

63, 5, 7, 9, …a₁₄ =

712, 17, 22, 27, …a₂₂ =

8−2, −3, −4, −5, …a₁₅ =

910, 13, 16, 19, …a₁₉ =

10−6, −9, −12, −15, …a₂₃ =

Arithmetic and geometric sequencesThe common difference

Name: Date:

Find the common difference of each sequence.

12, 4, 6, 8, 10, …d =

2−2, 0, 2, 4, 6, …d =

32, 9, 16, 23, 30, …d =

40, −1, −2, −3, −4, …d =

510, 11, 12, 13, 14, …d =

6−5, −13, −21, −29, −37, …d =

71, 0, −1, −2, −3, …d =

84, 6, 8, 10, 12, …d =

9−4, 0, 4, 8, 12, …d =

1012, 9, 6, 3, 0, …d =

Arithmetic and geometric sequencesThe nth term of a geometric sequence

Name: Date:

Find the term shown for each geometric sequence.

11, 3, 9, …a₇ =

26, 12, 24, …a₇ =

38, −16, 32, …a₆ =

47, −14, 28, …a₈ =

55, 10, 20, …a₉ =

61, 3, 9, …a₆ =

72, 4, 8, …a₈ =

86, −12, 24, …a₉ =

95, 15, 45, …a₇ =

103, −6, 12, …a₈ =

Arithmetic and geometric sequencesThe common ratio

Name: Date:

Find the common ratio of each sequence.

18, 40, 200, …r =

21, −4, 16, …r =

31, 5, 25, …r =

42, −8, 32, …r =

54, 12, 36, …r =

61, 6, 36, …r =

73, 9, 27, …r =

84, −16, 64, …r =

97, 35, 175, …r =

101, −2, 4, …r =

Power Pack · SequencesAnswer key

Arithmetic: nth term

1. 6, −1, −8, −15, … the 25th term = −1622. 0, 3, 6, 9, … the 25th term = 723. 9, 13, 17, 21, … the 19th term = 814. 12, 16, 20, 24, … the 15th term = 685. −7, −9, −11, −13, … the 23rd term = −516. 3, 5, 7, 9, … the 14th term = 297. 12, 17, 22, 27, … the 22nd term = 1178. −2, −3, −4, −5, … the 15th term = −169. 10, 13, 16, 19, … the 19th term = 6410. −6, −9, −12, −15, … the 23rd term = −72

Arithmetic: common difference

1. 2, 4, 6, 8, 10, … the common difference = 22. −2, 0, 2, 4, 6, … the common difference = 23. 2, 9, 16, 23, 30, … the common difference = 74. 0, −1, −2, −3, −4, … the common difference = −15. 10, 11, 12, 13, 14, … the common difference = 16. −5, −13, −21, −29, −37, … the common difference = −87. 1, 0, −1, −2, −3, … the common difference = −18. 4, 6, 8, 10, 12, … the common difference = 29. −4, 0, 4, 8, 12, … the common difference = 410. 12, 9, 6, 3, 0, … the common difference = −3

Geometric: nth term

1. 1, 3, 9, … the 7th term = 7292. 6, 12, 24, … the 7th term = 3843. 8, −16, 32, … the 6th term = −2564. 7, −14, 28, … the 8th term = −8965. 5, 10, 20, … the 9th term = 12806. 1, 3, 9, … the 6th term = 2437. 2, 4, 8, … the 8th term = 2568. 6, −12, 24, … the 9th term = 15369. 5, 15, 45, … the 7th term = 364510. 3, −6, 12, … the 8th term = −384

Geometric: common ratio

1. 8, 40, 200, … the common ratio = 52. 1, −4, 16, … the common ratio = −43. 1, 5, 25, … the common ratio = 54. 2, −8, 32, … the common ratio = −45. 4, 12, 36, … the common ratio = 36. 1, 6, 36, … the common ratio = 67. 3, 9, 27, … the common ratio = 38. 4, −16, 64, … the common ratio = −49. 7, 35, 175, … the common ratio = 510. 1, −2, 4, … the common ratio = −2

Sequences

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