Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 1 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence −1, −2, −3, −4, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n
- d = −2 − (−1) = −1
- Tₙ = a + (n − 1)d = −1 + (n − 1) × −1 = −n
2.For the arithmetic sequence 2, −1, −4, −7, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 5
- d = −1 − 2 = −3
- Tₙ = a + (n − 1)d = 2 + (n − 1) × −3 = −3n + 5
3.Find the 8th term of the arithmetic sequence 19, 16, 13, 10, …
Answer: −2
- a = 19, d = −3
- T8 = 19 + 7 × −3 = −2
4.Find the 28th term of the arithmetic sequence 5, 13, 21, 29, …
Answer: 221
- a = 5, d = 8
- T28 = 5 + 27 × 8 = 221
5.Find the 17th term of the arithmetic sequence −3, −2, −1, 0, …
Answer: 13
- a = −3, d = 1
- T17 = −3 + 16 × 1 = 13
6.Find the 25th term of the arithmetic sequence 8, 5, 2, −1, …
Answer: −64
- a = 8, d = −3
- T25 = 8 + 24 × −3 = −64
7.Find the 21th term of the arithmetic sequence 20, 17, 14, 11, …
Answer: −40
- a = 20, d = −3
- T21 = 20 + 20 × −3 = −40
8.For the arithmetic sequence 7, 13, 19, 25, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 1
- d = 13 − 7 = 6
- Tₙ = a + (n − 1)d = 7 + (n − 1) × 6 = 6n + 1
9.Find the 28th term of the arithmetic sequence 8, 4, 0, −4, …
Answer: −100
- a = 8, d = −4
- T28 = 8 + 27 × −4 = −100
10.For the arithmetic sequence 17, 26, 35, 44, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 8
- d = 26 − 17 = 9
- Tₙ = a + (n − 1)d = 17 + (n − 1) × 9 = 9n + 8
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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