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Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers

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

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Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers

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

1.Find the 7th term of the geometric sequence 8, 24, 72, 216, …

Answer: 5832

  1. a = 8, r = 3
  2. T7 = 8 × 36 = 5832
2.Find the sum of the first 7 terms of the geometric sequence −4, −20, −100, −500, …

Answer: −78124

  1. Sₙ = a(rⁿ − 1) ÷ (r − 1)
  2. = −4 × (57 − 1) ÷ (5 − 1)
  3. = −78124
3.Find the sum of the first 25 terms of the arithmetic sequence −9, 0, 9, 18, …

Answer: 2475

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 25/2 × (2 × −9 + 24 × 9)
  3. = 2475
4.For the arithmetic sequence −8, 1, 10, 19, …, write the common difference and the rule for the nth term.

Answer: d = 9; Tₙ = 9n − 17

  1. d = 1 − (−8) = 9
  2. Tₙ = a + (n − 1)d = −8 + (n − 1) × 9 = 9n − 17
5.Find the sum of the first 14 terms of the arithmetic sequence 19, 17, 15, 13, …

Answer: 84

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 14/2 × (2 × 19 + 13 × −2)
  3. = 84
6.Find the sum of the first 29 terms of the arithmetic sequence 5, 12, 19, 26, …

Answer: 2987

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 29/2 × (2 × 5 + 28 × 7)
  3. = 2987
7.Find the sum of the first 18 terms of the arithmetic sequence 16, 12, 8, 4, …

Answer: −324

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 18/2 × (2 × 16 + 17 × −4)
  3. = −324
8.Find the sum of the first 24 terms of the arithmetic sequence −8, −10, −12, −14, …

Answer: −744

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 24/2 × (2 × −8 + 23 × −2)
  3. = −744
9.Find the 20th term of the arithmetic sequence 4, 12, 20, 28, …

Answer: 156

  1. a = 4, d = 8
  2. T20 = 4 + 19 × 8 = 156
10.Find the sum of the first 8 terms of the arithmetic sequence 5, 8, 11, 14, …

Answer: 124

  1. Sₙ = n/2 × (2a + (n − 1)d)
  2. = 8/2 × (2 × 5 + 7 × 3)
  3. = 124
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