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Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 4 — Answers

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

1.Find the sum of the first 7 terms of the geometric sequence 1, 2, 4, 8, …

Answer: 127

  1. Sₙ = a(rⁿ − 1) ÷ (r − 1)
  2. = 1 × (27 − 1) ÷ (2 − 1)
  3. = 127
2.Find the 7th term of the geometric sequence 7, 28, 112, 448, …

Answer: 28672

  1. a = 7, r = 4
  2. T7 = 7 × 46 = 28672
3.For the arithmetic sequence 17, 23, 29, 35, …, write the common difference and the rule for the nth term.

Answer: d = 6; Tₙ = 6n + 11

  1. d = 23 − 17 = 6
  2. Tₙ = a + (n − 1)d = 17 + (n − 1) × 6 = 6n + 11
4.Find the sum of the first 26 terms of the arithmetic sequence −10, −15, −20, −25, …

Answer: −1885

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 26/2 × (2 × −10 + 25 × −5)
  3. = −1885
5.For the arithmetic sequence 1, 10, 19, 28, …, write the common difference and the rule for the nth term.

Answer: d = 9; Tₙ = 9n − 8

  1. d = 10 − 1 = 9
  2. Tₙ = a + (n − 1)d = 1 + (n − 1) × 9 = 9n − 8
6.For the geometric sequence 4, 16, 64, 256, …, write the common ratio and the rule for the nth term.

Answer: r = 4; Tₙ = 4 × 4n − 1

  1. r = 16 ÷ 4 = 4
7.Find the 8th term of the geometric sequence 3, 15, 75, 375, …

Answer: 234375

  1. a = 3, r = 5
  2. T8 = 3 × 57 = 234375
8.Find the 10th term of the arithmetic sequence 11, 18, 25, 32, …

Answer: 74

  1. a = 11, d = 7
  2. T10 = 11 + 9 × 7 = 74
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 × (−2)n − 1

  1. r = −14 ÷ 7 = −2
10.Find the 30th term of the arithmetic sequence 18, 24, 30, 36, …

Answer: 192

  1. a = 18, d = 6
  2. T30 = 18 + 29 × 6 = 192
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