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10th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — Answers

Answer sheet with worked solutions for the 10th Grade sequences & series worksheet.

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10th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — Answers

Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.

1.For the arithmetic sequence 18, 24, 30, 36, …, write the common difference and the rule for the nth term.

Answer: d = 6; Tₙ = 6n + 12

  1. d = 24 − 18 = 6
  2. Tₙ = a + (n − 1)d = 18 + (n − 1) × 6 = 6n + 12
2.Find the 13th term of the arithmetic sequence 4, 1, −2, −5, …

Answer: −32

  1. a = 4, d = −3
  2. T13 = 4 + 12 × −3 = −32
3.For the arithmetic sequence −1, 2, 5, 8, …, write the common difference and the rule for the nth term.

Answer: d = 3; Tₙ = 3n − 4

  1. d = 2 − (−1) = 3
  2. Tₙ = a + (n − 1)d = −1 + (n − 1) × 3 = 3n − 4
4.For the arithmetic sequence 6, 15, 24, 33, …, write the common difference and the rule for the nth term.

Answer: d = 9; Tₙ = 9n − 3

  1. d = 15 − 6 = 9
  2. Tₙ = a + (n − 1)d = 6 + (n − 1) × 9 = 9n − 3
5.For the arithmetic sequence 10, 16, 22, 28, …, write the common difference and the rule for the nth term.

Answer: d = 6; Tₙ = 6n + 4

  1. d = 16 − 10 = 6
  2. Tₙ = a + (n − 1)d = 10 + (n − 1) × 6 = 6n + 4
6.Find the 30th term of the arithmetic sequence 9, 8, 7, 6, …

Answer: −20

  1. a = 9, d = −1
  2. T30 = 9 + 29 × −1 = −20
7.Find the 12th term of the arithmetic sequence −8, −5, −2, 1, …

Answer: 25

  1. a = −8, d = 3
  2. T12 = −8 + 11 × 3 = 25
8.Find the 28th term of the arithmetic sequence 10, 15, 20, 25, …

Answer: 145

  1. a = 10, d = 5
  2. T28 = 10 + 27 × 5 = 145
9.Find the 12th term of the arithmetic sequence 7, 12, 17, 22, …

Answer: 62

  1. a = 7, d = 5
  2. T12 = 7 + 11 × 5 = 62
10.For the arithmetic sequence 4, 9, 14, 19, …, write the common difference and the rule for the nth term.

Answer: d = 5; Tₙ = 5n − 1

  1. d = 9 − 4 = 5
  2. Tₙ = a + (n − 1)d = 4 + (n − 1) × 5 = 5n − 1
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