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Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers

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

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & Series

Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers

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

1.Find the sum of the first 20 terms of the arithmetic sequence 11, 10, 9, 8, …

Answer: 30

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 20/2 × (2 × 11 + 19 × −1)
  3. = 30
2.Find the sum of the first 8 terms of the arithmetic sequence −10, −8, −6, −4, …

Answer: −24

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 8/2 × (2 × −10 + 7 × 2)
  3. = −24
3.Find the sum of the first 6 terms of the geometric sequence 5, 25, 125, 625, …

Answer: 19530

  1. Sₙ = a(rⁿ − 1) ÷ (r − 1)
  2. = 5 × (56 − 1) ÷ (5 − 1)
  3. = 19530
4.For the geometric sequence 1, 3, 9, 27, …, write the common ratio and the rule for the nth term.

Answer: r = 3; Tₙ = 1 × 3n − 1

  1. r = 3 ÷ 1 = 3
5.Find the sum of the first 29 terms of the arithmetic sequence −8, −11, −14, −17, …

Answer: −1450

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 29/2 × (2 × −8 + 28 × −3)
  3. = −1450
6.Find the 10th term of the arithmetic sequence 3, 5, 7, 9, …

Answer: 21

  1. a = 3, d = 2
  2. T10 = 3 + 9 × 2 = 21
7.Find the sum of the first 6 terms of the geometric sequence −5, −25, −125, −625, …

Answer: −19530

  1. Sₙ = a(rⁿ − 1) ÷ (r − 1)
  2. = −5 × (56 − 1) ÷ (5 − 1)
  3. = −19530
8.Find the sum of the first 24 terms of the arithmetic sequence 9, 16, 23, 30, …

Answer: 2148

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 24/2 × (2 × 9 + 23 × 7)
  3. = 2148
9.For the geometric sequence 7, 14, 28, 56, …, write the common ratio and the rule for the nth term.

Answer: r = 2; Tₙ = 7 × 2n − 1

  1. r = 14 ÷ 7 = 2
10.Find the sum of the first 6 terms of the geometric sequence 3, 12, 48, 192, …

Answer: 4095

  1. Sₙ = a(rⁿ − 1) ÷ (r − 1)
  2. = 3 × (46 − 1) ÷ (4 − 1)
  3. = 4095
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