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Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 12 sequences & series worksheet.

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Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — Answers

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

1.Find the 23th term of the arithmetic sequence −5, 1, 7, 13, …

Answer: 127

  1. a = −5, d = 6
  2. T23 = −5 + 22 × 6 = 127
2.Find the 28th term of the arithmetic sequence 20, 19, 18, 17, …

Answer: −7

  1. a = 20, d = −1
  2. T28 = 20 + 27 × −1 = −7
3.Find the 25th term of the arithmetic sequence 16, 17, 18, 19, …

Answer: 40

  1. a = 16, d = 1
  2. T25 = 16 + 24 × 1 = 40
4.Find the 29th term of the arithmetic sequence 15, 22, 29, 36, …

Answer: 211

  1. a = 15, d = 7
  2. T29 = 15 + 28 × 7 = 211
5.Find the 19th term of the arithmetic sequence 19, 28, 37, 46, …

Answer: 181

  1. a = 19, d = 9
  2. T19 = 19 + 18 × 9 = 181
6.For the arithmetic sequence 10, 13, 16, 19, …, write the common difference and the rule for the nth term.

Answer: d = 3; Tₙ = 3n + 7

  1. d = 13 − 10 = 3
  2. Tₙ = a + (n − 1)d = 10 + (n − 1) × 3 = 3n + 7
7.For the arithmetic sequence 13, 22, 31, 40, …, write the common difference and the rule for the nth term.

Answer: d = 9; Tₙ = 9n + 4

  1. d = 22 − 13 = 9
  2. Tₙ = a + (n − 1)d = 13 + (n − 1) × 9 = 9n + 4
8.Find the 26th term of the arithmetic sequence −9, −5, −1, 3, …

Answer: 91

  1. a = −9, d = 4
  2. T26 = −9 + 25 × 4 = 91
9.For the arithmetic sequence 14, 10, 6, 2, …, write the common difference and the rule for the nth term.

Answer: d = −4; Tₙ = −4n + 18

  1. d = 10 − 14 = −4
  2. Tₙ = a + (n − 1)d = 14 + (n − 1) × −4 = −4n + 18
10.For the arithmetic sequence 1, 8, 15, 22, …, write the common difference and the rule for the nth term.

Answer: d = 7; Tₙ = 7n − 6

  1. d = 8 − 1 = 7
  2. Tₙ = a + (n − 1)d = 1 + (n − 1) × 7 = 7n − 6
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