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 −3, −6, −9, −12, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n
- d = −6 − (−3) = −3
- Tₙ = a + (n − 1)d = −3 + (n − 1) × −3 = −3n
2.For the arithmetic sequence 1, −4, −9, −14, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 6
- d = −4 − 1 = −5
- Tₙ = a + (n − 1)d = 1 + (n − 1) × −5 = −5n + 6
3.Find the 9th term of the arithmetic sequence −8, −4, 0, 4, …
Answer: 24
- a = −8, d = 4
- T9 = −8 + 8 × 4 = 24
4.For the arithmetic sequence 9, 8, 7, 6, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 10
- d = 8 − 9 = −1
- Tₙ = a + (n − 1)d = 9 + (n − 1) × −1 = −n + 10
5.Find the 14th term of the arithmetic sequence −5, 0, 5, 10, …
Answer: 60
- a = −5, d = 5
- T14 = −5 + 13 × 5 = 60
6.For the arithmetic sequence 16, 15, 14, 13, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 17
- d = 15 − 16 = −1
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −1 = −n + 17
7.For the arithmetic sequence 7, 12, 17, 22, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 2
- d = 12 − 7 = 5
- Tₙ = a + (n − 1)d = 7 + (n − 1) × 5 = 5n + 2
8.For the arithmetic sequence 13, 15, 17, 19, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 11
- d = 15 − 13 = 2
- Tₙ = a + (n − 1)d = 13 + (n − 1) × 2 = 2n + 11
9.For the arithmetic sequence 8, 4, 0, −4, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 12
- d = 4 − 8 = −4
- Tₙ = a + (n − 1)d = 8 + (n − 1) × −4 = −4n + 12
10.For the arithmetic sequence 20, 19, 18, 17, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 21
- d = 19 − 20 = −1
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −1 = −n + 21
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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