Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 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.Find the sum of the first 6 terms of the geometric sequence 8, 32, 128, 512, …
Answer: 10920
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (46 − 1) ÷ (4 − 1)
- = 10920
2.For the geometric sequence 1, 4, 16, 64, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 1 × 4n − 1
- r = 4 ÷ 1 = 4
3.For the arithmetic sequence −1, 1, 3, 5, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 3
- d = 1 − (−1) = 2
- Tₙ = a + (n − 1)d = −1 + (n − 1) × 2 = 2n − 3
4.For the geometric sequence 8, 32, 128, 512, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 8 × 4n − 1
- r = 32 ÷ 8 = 4
5.Find the 7th term of the geometric sequence −4, 8, −16, 32, …
Answer: −256
- a = −4, r = −2
- T7 = −4 × (−2)6 = −256
6.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
7.For the geometric sequence −3, −12, −48, −192, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = −3 × 4n − 1
- r = −12 ÷ (−3) = 4
8.Find the sum of the first 7 terms of the geometric sequence 6, 18, 54, 162, …
Answer: 6558
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (37 − 1) ÷ (3 − 1)
- = 6558
9.Find the 17th term of the arithmetic sequence −5, −1, 3, 7, …
Answer: 59
- a = −5, d = 4
- T17 = −5 + 16 × 4 = 59
10.For the geometric sequence 8, 16, 32, 64, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 8 × 2n − 1
- r = 16 ÷ 8 = 2
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.