Year 10 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 26th term of the arithmetic sequence 2, −3, −8, −13, …
Answer: −123
- a = 2, d = −5
- T26 = 2 + 25 × −5 = −123
2.Find the 26th term of the arithmetic sequence 17, 12, 7, 2, …
Answer: −108
- a = 17, d = −5
- T26 = 17 + 25 × −5 = −108
3.For the arithmetic sequence −4, 0, 4, 8, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 8
- d = 0 − (−4) = 4
- Tₙ = a + (n − 1)d = −4 + (n − 1) × 4 = 4n − 8
4.For the arithmetic sequence 15, 16, 17, 18, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 14
- d = 16 − 15 = 1
- Tₙ = a + (n − 1)d = 15 + (n − 1) × 1 = n + 14
5.For the arithmetic sequence 16, 13, 10, 7, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 19
- d = 13 − 16 = −3
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −3 = −3n + 19
6.Find the 13th term of the arithmetic sequence −8, −11, −14, −17, …
Answer: −44
- a = −8, d = −3
- T13 = −8 + 12 × −3 = −44
7.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
8.Find the 11th term of the arithmetic sequence 19, 27, 35, 43, …
Answer: 99
- a = 19, d = 8
- T11 = 19 + 10 × 8 = 99
9.For the arithmetic sequence 6, 4, 2, 0, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 8
- d = 4 − 6 = −2
- Tₙ = a + (n − 1)d = 6 + (n − 1) × −2 = −2n + 8
10.For the arithmetic sequence 14, 18, 22, 26, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 10
- d = 18 − 14 = 4
- Tₙ = a + (n − 1)d = 14 + (n − 1) × 4 = 4n + 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.
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