Year 13 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 13 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Sequences & SeriesYear 13 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.For the geometric sequence 3, −6, 12, −24, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 3 × (−2)n − 1
- r = −6 ÷ 3 = −2
2.For the arithmetic sequence −2, 6, 14, 22, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 10
- d = 6 − (−2) = 8
- Tₙ = a + (n − 1)d = −2 + (n − 1) × 8 = 8n − 10
3.Find the sum of the first 13 terms of the arithmetic sequence 18, 14, 10, 6, …
Answer: −78
- Sₙ = n/2 × (2a + (n − 1)d)
- = 13/2 × (2 × 18 + 12 × −4)
- = −78
4.Find the 22th term of the arithmetic sequence 16, 10, 4, −2, …
Answer: −110
- a = 16, d = −6
- T22 = 16 + 21 × −6 = −110
5.Find the 11th term of the arithmetic sequence 11, 17, 23, 29, …
Answer: 71
- a = 11, d = 6
- T11 = 11 + 10 × 6 = 71
6.For the arithmetic sequence 16, 15, 14, 13, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 17
- d = 15 − 16 = −1
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −1 = −n + 17
7.For the geometric sequence −3, −12, −48, −192, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = −3 × 4n − 1
- r = −12 ÷ (−3) = 4
8.Find the 6th term of the geometric sequence 4, 8, 16, 32, …
Answer: 128
- a = 4, r = 2
- T6 = 4 × 25 = 128
9.Find the sum of the first 27 terms of the arithmetic sequence 15, 19, 23, 27, …
Answer: 1809
- Sₙ = n/2 × (2a + (n − 1)d)
- = 27/2 × (2 × 15 + 26 × 4)
- = 1809
10.Find the sum of the first 11 terms of the arithmetic sequence 1, 6, 11, 16, …
Answer: 286
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × 1 + 10 × 5)
- = 286
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
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