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Year 13 Arithmetic and Geometric Sequences Worksheet — Level 1 — Answers

Answer sheet with worked solutions for the Year 13 sequences & series worksheet.

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Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Sequences & Series

Year 13 Arithmetic and Geometric Sequences Worksheet — Level 1 — Answers

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

1.For the arithmetic sequence 7, 10, 13, 16, …, write the common difference and the rule for the nth term.

Answer: d = 3; Tₙ = 3n + 4

  1. d = 10 − 7 = 3
  2. Tₙ = a + (n − 1)d = 7 + (n − 1) × 3 = 3n + 4
2.For the arithmetic sequence 9, 18, 27, 36, …, write the common difference and the rule for the nth term.

Answer: d = 9; Tₙ = 9n

  1. d = 18 − 9 = 9
  2. Tₙ = a + (n − 1)d = 9 + (n − 1) × 9 = 9n
3.Find the 22th term of the arithmetic sequence 11, 13, 15, 17, …

Answer: 53

  1. a = 11, d = 2
  2. T22 = 11 + 21 × 2 = 53
4.Find the 23th term of the arithmetic sequence −8, −2, 4, 10, …

Answer: 124

  1. a = −8, d = 6
  2. T23 = −8 + 22 × 6 = 124
5.Find the 18th term of the arithmetic sequence 3, 6, 9, 12, …

Answer: 54

  1. a = 3, d = 3
  2. T18 = 3 + 17 × 3 = 54
6.For the arithmetic sequence 3, 2, 1, 0, …, write the common difference and the rule for the nth term.

Answer: d = −1; Tₙ = −n + 4

  1. d = 2 − 3 = −1
  2. Tₙ = a + (n − 1)d = 3 + (n − 1) × −1 = −n + 4
7.Find the 14th term of the arithmetic sequence 8, 5, 2, −1, …

Answer: −31

  1. a = 8, d = −3
  2. T14 = 8 + 13 × −3 = −31
8.For the arithmetic sequence 10, 15, 20, 25, …, write the common difference and the rule for the nth term.

Answer: d = 5; Tₙ = 5n + 5

  1. d = 15 − 10 = 5
  2. Tₙ = a + (n − 1)d = 10 + (n − 1) × 5 = 5n + 5
9.For the arithmetic sequence 14, 21, 28, 35, …, write the common difference and the rule for the nth term.

Answer: d = 7; Tₙ = 7n + 7

  1. d = 21 − 14 = 7
  2. Tₙ = a + (n − 1)d = 14 + (n − 1) × 7 = 7n + 7
10.Find the 23th term of the arithmetic sequence −10, −16, −22, −28, …

Answer: −142

  1. a = −10, d = −6
  2. T23 = −10 + 22 × −6 = −142
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