Year 10 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — 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 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence −5, −3, −1, 1, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 7
- d = −3 − (−5) = 2
- Tₙ = a + (n − 1)d = −5 + (n − 1) × 2 = 2n − 7
2.Find the 23th term of the arithmetic sequence −5, 2, 9, 16, …
Answer: 149
- a = −5, d = 7
- T23 = −5 + 22 × 7 = 149
3.Find the 14th term of the arithmetic sequence 19, 17, 15, 13, …
Answer: −7
- a = 19, d = −2
- T14 = 19 + 13 × −2 = −7
4.Find the 9th term of the arithmetic sequence 5, 2, −1, −4, …
Answer: −19
- a = 5, d = −3
- T9 = 5 + 8 × −3 = −19
5.For the arithmetic sequence −8, 1, 10, 19, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 17
- d = 1 − (−8) = 9
- Tₙ = a + (n − 1)d = −8 + (n − 1) × 9 = 9n − 17
6.For the arithmetic sequence −7, −9, −11, −13, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 5
- d = −9 − (−7) = −2
- Tₙ = a + (n − 1)d = −7 + (n − 1) × −2 = −2n − 5
7.Find the 28th term of the arithmetic sequence 16, 18, 20, 22, …
Answer: 70
- a = 16, d = 2
- T28 = 16 + 27 × 2 = 70
8.For the arithmetic sequence 13, 12, 11, 10, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 14
- d = 12 − 13 = −1
- Tₙ = a + (n − 1)d = 13 + (n − 1) × −1 = −n + 14
9.For the arithmetic sequence −2, −8, −14, −20, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 4
- d = −8 − (−2) = −6
- Tₙ = a + (n − 1)d = −2 + (n − 1) × −6 = −6n + 4
10.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
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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