Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 12 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & SeriesYear 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 6 terms of the geometric sequence −4, 8, −16, 32, …
Answer: 84
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × ((−2)6 − 1) ÷ (−2 − 1)
- = 84
2.Find the 5th term of the geometric sequence 2, 6, 18, 54, …
Answer: 162
- a = 2, r = 3
- T5 = 2 × 34 = 162
3.Find the sum of the first 9 terms of the arithmetic sequence 20, 28, 36, 44, …
Answer: 468
- Sₙ = n/2 × (2a + (n − 1)d)
- = 9/2 × (2 × 20 + 8 × 8)
- = 468
4.Find the 18th term of the arithmetic sequence 4, 0, −4, −8, …
Answer: −64
- a = 4, d = −4
- T18 = 4 + 17 × −4 = −64
5.Find the sum of the first 27 terms of the arithmetic sequence −2, 4, 10, 16, …
Answer: 2052
- Sₙ = n/2 × (2a + (n − 1)d)
- = 27/2 × (2 × −2 + 26 × 6)
- = 2052
6.For the geometric sequence 5, 20, 80, 320, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 5 × 4n − 1
- r = 20 ÷ 5 = 4
7.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
- r = −14 ÷ 7 = −2
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 12th term of the arithmetic sequence 11, 12, 13, 14, …
Answer: 22
- a = 11, d = 1
- T12 = 11 + 11 × 1 = 22
10.For the arithmetic sequence 0, 9, 18, 27, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 9
- d = 9 − 0 = 9
- Tₙ = a + (n − 1)d = 0 + (n − 1) × 9 = 9n − 9
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.
- Celebrate what went well first, then pick one thing to work on next.
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