Year 10 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 0, 3, 6, 9, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n − 3
- d = 3 − 0 = 3
- Tₙ = a + (n − 1)d = 0 + (n − 1) × 3 = 3n − 3
2.Find the sum of the first 11 terms of the arithmetic sequence 7, 10, 13, 16, …
Answer: 242
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × 7 + 10 × 3)
- = 242
3.For the arithmetic sequence −4, −5, −6, −7, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n − 3
- d = −5 − (−4) = −1
- Tₙ = a + (n − 1)d = −4 + (n − 1) × −1 = −n − 3
4.For the geometric sequence −1, −2, −4, −8, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −1 × 2n − 1
- r = −2 ÷ (−1) = 2
5.Find the sum of the first 16 terms of the arithmetic sequence 5, 8, 11, 14, …
Answer: 440
- Sₙ = n/2 × (2a + (n − 1)d)
- = 16/2 × (2 × 5 + 15 × 3)
- = 440
6.Find the 7th term of the geometric sequence −3, −9, −27, −81, …
Answer: −2187
- a = −3, r = 3
- T7 = −3 × 36 = −2187
7.Find the 6th term of the geometric sequence 6, 24, 96, 384, …
Answer: 6144
- a = 6, r = 4
- T6 = 6 × 45 = 6144
8.Find the 11th term of the arithmetic sequence 0, 2, 4, 6, …
Answer: 20
- a = 0, d = 2
- T11 = 0 + 10 × 2 = 20
9.For the geometric sequence 6, 30, 150, 750, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 6 × 5n − 1
- r = 30 ÷ 6 = 5
10.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
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.