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 13, 22, 31, 40, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 4
- d = 22 − 13 = 9
- Tₙ = a + (n − 1)d = 13 + (n − 1) × 9 = 9n + 4
2.Find the 9th term of the arithmetic sequence 0, 4, 8, 12, …
Answer: 32
- a = 0, d = 4
- T9 = 0 + 8 × 4 = 32
3.Find the 11th term of the arithmetic sequence 18, 13, 8, 3, …
Answer: −32
- a = 18, d = −5
- T11 = 18 + 10 × −5 = −32
4.For the arithmetic sequence 15, 12, 9, 6, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 18
- d = 12 − 15 = −3
- Tₙ = a + (n − 1)d = 15 + (n − 1) × −3 = −3n + 18
5.Find the 28th term of the arithmetic sequence 15, 21, 27, 33, …
Answer: 177
- a = 15, d = 6
- T28 = 15 + 27 × 6 = 177
6.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
7.For the arithmetic sequence 10, 8, 6, 4, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 12
- d = 8 − 10 = −2
- Tₙ = a + (n − 1)d = 10 + (n − 1) × −2 = −2n + 12
8.For the arithmetic sequence 16, 25, 34, 43, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 7
- d = 25 − 16 = 9
- Tₙ = a + (n − 1)d = 16 + (n − 1) × 9 = 9n + 7
9.For the arithmetic sequence 0, 7, 14, 21, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 7
- d = 7 − 0 = 7
- Tₙ = a + (n − 1)d = 0 + (n − 1) × 7 = 7n − 7
10.For the arithmetic sequence 15, 19, 23, 27, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 11
- d = 19 − 15 = 4
- Tₙ = a + (n − 1)d = 15 + (n − 1) × 4 = 4n + 11
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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