Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 22 terms of the arithmetic sequence 9, 6, 3, 0, …
Answer: −495
- Sₙ = n/2 × (2a + (n − 1)d)
- = 22/2 × (2 × 9 + 21 × −3)
- = −495
2.For the geometric sequence −2, −6, −18, −54, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −2 × 3n − 1
- r = −6 ÷ (−2) = 3
3.Find the sum of the first 6 terms of the geometric sequence −1, −3, −9, −27, …
Answer: −364
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (36 − 1) ÷ (3 − 1)
- = −364
4.Find the 7th term of the geometric sequence −1, −3, −9, −27, …
Answer: −729
- a = −1, r = 3
- T7 = −1 × 36 = −729
5.Find the 29th term of the arithmetic sequence 9, 3, −3, −9, …
Answer: −159
- a = 9, d = −6
- T29 = 9 + 28 × −6 = −159
6.For the arithmetic sequence 8, 6, 4, 2, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 10
- d = 6 − 8 = −2
- Tₙ = a + (n − 1)d = 8 + (n − 1) × −2 = −2n + 10
7.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
- r = 3 ÷ 1 = 3
8.Find the sum of the first 8 terms of the arithmetic sequence 18, 23, 28, 33, …
Answer: 284
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × 18 + 7 × 5)
- = 284
9.For the arithmetic sequence 11, 20, 29, 38, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 2
- d = 20 − 11 = 9
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 9 = 9n + 2
10.Find the sum of the first 8 terms of the geometric sequence 3, 12, 48, 192, …
Answer: 65535
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 3 × (48 − 1) ÷ (4 − 1)
- = 65535
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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