Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 9th term of the geometric sequence 5, 15, 45, 135, …
Answer: 32805
- a = 5, r = 3
- T9 = 5 × 38 = 32805
2.Find the sum of the first 21 terms of the arithmetic sequence 14, 10, 6, 2, …
Answer: −546
- Sₙ = n/2 × (2a + (n − 1)d)
- = 21/2 × (2 × 14 + 20 × −4)
- = −546
3.For the arithmetic sequence 9, 11, 13, 15, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 7
- d = 11 − 9 = 2
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 2 = 2n + 7
4.Find the sum of the first 7 terms of the geometric sequence −5, −25, −125, −625, …
Answer: −97655
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (57 − 1) ÷ (5 − 1)
- = −97655
5.Find the 6th term of the geometric sequence −1, −3, −9, −27, …
Answer: −243
- a = −1, r = 3
- T6 = −1 × 35 = −243
6.Find the 14th term of the arithmetic sequence 5, 8, 11, 14, …
Answer: 44
- a = 5, d = 3
- T14 = 5 + 13 × 3 = 44
7.For the geometric sequence 8, 40, 200, 1000, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 8 × 5n − 1
- r = 40 ÷ 8 = 5
8.Find the 15th term of the arithmetic sequence 3, −2, −7, −12, …
Answer: −67
- a = 3, d = −5
- T15 = 3 + 14 × −5 = −67
9.Find the sum of the first 9 terms of the geometric sequence 1, 5, 25, 125, …
Answer: 488281
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (59 − 1) ÷ (5 − 1)
- = 488281
10.For the arithmetic sequence 1, 9, 17, 25, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 7
- d = 9 − 1 = 8
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 8 = 8n − 7
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.