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 28th term of the arithmetic sequence 18, 16, 14, 12, …
Answer: −36
- a = 18, d = −2
- T28 = 18 + 27 × −2 = −36
2.For the arithmetic sequence 14, 23, 32, 41, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 5
- d = 23 − 14 = 9
- Tₙ = a + (n − 1)d = 14 + (n − 1) × 9 = 9n + 5
3.Find the 30th term of the arithmetic sequence 16, 25, 34, 43, …
Answer: 277
- a = 16, d = 9
- T30 = 16 + 29 × 9 = 277
4.Find the 11th term of the arithmetic sequence 3, 7, 11, 15, …
Answer: 43
- a = 3, d = 4
- T11 = 3 + 10 × 4 = 43
5.For the arithmetic sequence −10, −15, −20, −25, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n − 5
- d = −15 − (−10) = −5
- Tₙ = a + (n − 1)d = −10 + (n − 1) × −5 = −5n − 5
6.Find the 21th term of the arithmetic sequence 5, 2, −1, −4, …
Answer: −55
- a = 5, d = −3
- T21 = 5 + 20 × −3 = −55
7.Find the 12th term of the arithmetic sequence 15, 11, 7, 3, …
Answer: −29
- a = 15, d = −4
- T12 = 15 + 11 × −4 = −29
8.Find the 19th term of the arithmetic sequence 4, 1, −2, −5, …
Answer: −50
- a = 4, d = −3
- T19 = 4 + 18 × −3 = −50
9.Find the 11th term of the arithmetic sequence 3, −2, −7, −12, …
Answer: −47
- a = 3, d = −5
- T11 = 3 + 10 × −5 = −47
10.For the arithmetic sequence 18, 26, 34, 42, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 10
- d = 26 − 18 = 8
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 8 = 8n + 10
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.
Great work. Here's what to try next: