Year 13 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — 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 1 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 23th term of the arithmetic sequence 17, 11, 5, −1, …
Answer: −115
- a = 17, d = −6
- T23 = 17 + 22 × −6 = −115
2.For the arithmetic sequence 10, 18, 26, 34, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 2
- d = 18 − 10 = 8
- Tₙ = a + (n − 1)d = 10 + (n − 1) × 8 = 8n + 2
3.For the arithmetic sequence 3, 9, 15, 21, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 3
- d = 9 − 3 = 6
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 6 = 6n − 3
4.For the arithmetic sequence −2, −5, −8, −11, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 1
- d = −5 − (−2) = −3
- Tₙ = a + (n − 1)d = −2 + (n − 1) × −3 = −3n + 1
5.For the arithmetic sequence 9, 16, 23, 30, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n + 2
- d = 16 − 9 = 7
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 7 = 7n + 2
6.Find the 27th term of the arithmetic sequence 14, 15, 16, 17, …
Answer: 40
- a = 14, d = 1
- T27 = 14 + 26 × 1 = 40
7.Find the 19th term of the arithmetic sequence 9, 13, 17, 21, …
Answer: 81
- a = 9, d = 4
- T19 = 9 + 18 × 4 = 81
8.For the arithmetic sequence 12, 11, 10, 9, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 13
- d = 11 − 12 = −1
- Tₙ = a + (n − 1)d = 12 + (n − 1) × −1 = −n + 13
9.For the arithmetic sequence 7, 2, −3, −8, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 12
- d = 2 − 7 = −5
- Tₙ = a + (n − 1)d = 7 + (n − 1) × −5 = −5n + 12
10.For the arithmetic sequence 20, 24, 28, 32, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 16
- d = 24 − 20 = 4
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 4 = 4n + 16
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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