Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 20, 18, 16, 14, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 22
- d = 18 − 20 = −2
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −2 = −2n + 22
2.Find the 13th term of the arithmetic sequence 13, 21, 29, 37, …
Answer: 109
- a = 13, d = 8
- T13 = 13 + 12 × 8 = 109
3.Find the sum of the first 6 terms of the geometric sequence −2, 4, −8, 16, …
Answer: 42
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −2 × ((−2)6 − 1) ÷ (−2 − 1)
- = 42
4.Find the sum of the first 10 terms of the arithmetic sequence 5, 7, 9, 11, …
Answer: 140
- Sₙ = n/2 × (2a + (n − 1)d)
- = 10/2 × (2 × 5 + 9 × 2)
- = 140
5.Find the 6th term of the geometric sequence −5, −10, −20, −40, …
Answer: −160
- a = −5, r = 2
- T6 = −5 × 25 = −160
6.For the arithmetic sequence 18, 14, 10, 6, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 22
- d = 14 − 18 = −4
- Tₙ = a + (n − 1)d = 18 + (n − 1) × −4 = −4n + 22
7.For the arithmetic sequence 11, 9, 7, 5, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 13
- d = 9 − 11 = −2
- Tₙ = a + (n − 1)d = 11 + (n − 1) × −2 = −2n + 13
8.Find the 9th term of the arithmetic sequence −1, 8, 17, 26, …
Answer: 71
- a = −1, d = 9
- T9 = −1 + 8 × 9 = 71
9.For the arithmetic sequence 3, 8, 13, 18, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 2
- d = 8 − 3 = 5
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 5 = 5n − 2
10.Find the sum of the first 7 terms of the geometric sequence 8, 32, 128, 512, …
Answer: 43688
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (47 − 1) ÷ (4 − 1)
- = 43688
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.
Great work. Here's what to try next: