Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — 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 1 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 1, −2, −5, −8, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 4
- d = −2 − 1 = −3
- Tₙ = a + (n − 1)d = 1 + (n − 1) × −3 = −3n + 4
2.For the arithmetic sequence −1, 7, 15, 23, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 9
- d = 7 − (−1) = 8
- Tₙ = a + (n − 1)d = −1 + (n − 1) × 8 = 8n − 9
3.Find the 16th term of the arithmetic sequence 9, 8, 7, 6, …
Answer: −6
- a = 9, d = −1
- T16 = 9 + 15 × −1 = −6
4.Find the 12th term of the arithmetic sequence 1, −3, −7, −11, …
Answer: −43
- a = 1, d = −4
- T12 = 1 + 11 × −4 = −43
5.For the arithmetic sequence 20, 15, 10, 5, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 25
- d = 15 − 20 = −5
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −5 = −5n + 25
6.For the arithmetic sequence −6, −7, −8, −9, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n − 5
- d = −7 − (−6) = −1
- Tₙ = a + (n − 1)d = −6 + (n − 1) × −1 = −n − 5
7.Find the 8th term of the arithmetic sequence 17, 22, 27, 32, …
Answer: 52
- a = 17, d = 5
- T8 = 17 + 7 × 5 = 52
8.For the arithmetic sequence 17, 19, 21, 23, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 15
- d = 19 − 17 = 2
- Tₙ = a + (n − 1)d = 17 + (n − 1) × 2 = 2n + 15
9.For the arithmetic sequence 0, 4, 8, 12, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 4
- d = 4 − 0 = 4
- Tₙ = a + (n − 1)d = 0 + (n − 1) × 4 = 4n − 4
10.For the arithmetic sequence 12, 9, 6, 3, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 15
- d = 9 − 12 = −3
- Tₙ = a + (n − 1)d = 12 + (n − 1) × −3 = −3n + 15
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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