Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 3 — 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 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence −1, −2, −4, −8, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −1 × 2n − 1
- r = −2 ÷ (−1) = 2
2.Find the sum of the first 9 terms of the geometric sequence 6, 12, 24, 48, …
Answer: 3066
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (29 − 1) ÷ (2 − 1)
- = 3066
3.Find the sum of the first 20 terms of the arithmetic sequence 17, 22, 27, 32, …
Answer: 1290
- Sₙ = n/2 × (2a + (n − 1)d)
- = 20/2 × (2 × 17 + 19 × 5)
- = 1290
4.Find the 8th term of the arithmetic sequence 7, 3, −1, −5, …
Answer: −21
- a = 7, d = −4
- T8 = 7 + 7 × −4 = −21
5.For the geometric sequence 6, 24, 96, 384, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 6 × 4n − 1
- r = 24 ÷ 6 = 4
6.Find the 7th term of the geometric sequence 4, 16, 64, 256, …
Answer: 16384
- a = 4, r = 4
- T7 = 4 × 46 = 16384
7.Find the sum of the first 27 terms of the arithmetic sequence −4, 0, 4, 8, …
Answer: 1296
- Sₙ = n/2 × (2a + (n − 1)d)
- = 27/2 × (2 × −4 + 26 × 4)
- = 1296
8.Find the sum of the first 11 terms of the arithmetic sequence −8, −13, −18, −23, …
Answer: −363
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × −8 + 10 × −5)
- = −363
9.Find the 9th term of the geometric sequence 7, 14, 28, 56, …
Answer: 1792
- a = 7, r = 2
- T9 = 7 × 28 = 1792
10.For the geometric sequence 1, 5, 25, 125, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 1 × 5n − 1
- r = 5 ÷ 1 = 5
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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