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.For the geometric sequence −5, −10, −20, −40, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −5 × 2n − 1
- r = −10 ÷ (−5) = 2
2.For the arithmetic sequence 6, 14, 22, 30, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 2
- d = 14 − 6 = 8
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 8 = 8n − 2
3.For the geometric sequence −3, 6, −12, 24, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = −3 × (−2)n − 1
- r = 6 ÷ (−3) = −2
4.Find the 8th term of the geometric sequence −1, 2, −4, 8, …
Answer: 128
- a = −1, r = −2
- T8 = −1 × (−2)7 = 128
5.Find the 16th term of the arithmetic sequence −8, −2, 4, 10, …
Answer: 82
- a = −8, d = 6
- T16 = −8 + 15 × 6 = 82
6.Find the 27th term of the arithmetic sequence 19, 23, 27, 31, …
Answer: 123
- a = 19, d = 4
- T27 = 19 + 26 × 4 = 123
7.Find the 6th term of the geometric sequence 3, 9, 27, 81, …
Answer: 729
- a = 3, r = 3
- T6 = 3 × 35 = 729
8.Find the sum of the first 8 terms of the geometric sequence 8, −16, 32, −64, …
Answer: −680
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × ((−2)8 − 1) ÷ (−2 − 1)
- = −680
9.Find the sum of the first 26 terms of the arithmetic sequence 4, 12, 20, 28, …
Answer: 2704
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 4 + 25 × 8)
- = 2704
10.Find the 15th term of the arithmetic sequence −5, −10, −15, −20, …
Answer: −75
- a = −5, d = −5
- T15 = −5 + 14 × −5 = −75
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.