Year 10 Arithmetic and Geometric Sequences Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 10 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Sequences & SeriesYear 10 Arithmetic and Geometric Sequences Worksheet — Level 1 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 20th term of the arithmetic sequence −3, −8, −13, −18, …
Answer: −98
- a = −3, d = −5
- T20 = −3 + 19 × −5 = −98
2.Find the 27th term of the arithmetic sequence −7, −4, −1, 2, …
Answer: 71
- a = −7, d = 3
- T27 = −7 + 26 × 3 = 71
3.For the arithmetic sequence 4, 2, 0, −2, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 6
- d = 2 − 4 = −2
- Tₙ = a + (n − 1)d = 4 + (n − 1) × −2 = −2n + 6
4.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
5.Find the 26th term of the arithmetic sequence 4, 5, 6, 7, …
Answer: 29
- a = 4, d = 1
- T26 = 4 + 25 × 1 = 29
6.Find the 28th term of the arithmetic sequence −4, 5, 14, 23, …
Answer: 239
- a = −4, d = 9
- T28 = −4 + 27 × 9 = 239
7.Find the 28th term of the arithmetic sequence 3, 5, 7, 9, …
Answer: 57
- a = 3, d = 2
- T28 = 3 + 27 × 2 = 57
8.Find the 14th term of the arithmetic sequence −3, 5, 13, 21, …
Answer: 101
- a = −3, d = 8
- T14 = −3 + 13 × 8 = 101
9.Find the 9th term of the arithmetic sequence 1, 2, 3, 4, …
Answer: 9
- a = 1, d = 1
- T9 = 1 + 8 × 1 = 9
10.For the arithmetic sequence 11, 18, 25, 32, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n + 4
- d = 18 − 11 = 7
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 7 = 7n + 4
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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