Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — 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 × (−2)n − 1
- r = 10 ÷ (−5) = −2
2.Find the 7th term of the geometric sequence 1, 5, 25, 125, …
Answer: 15625
- a = 1, r = 5
- T7 = 1 × 56 = 15625
3.For the geometric sequence −2, −10, −50, −250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −2 × 5n − 1
- r = −10 ÷ (−2) = 5
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 × (−2)n − 1
- r = −2 ÷ 1 = −2
5.Find the sum of the first 20 terms of the arithmetic sequence 18, 21, 24, 27, …
Answer: 930
- Sₙ = n/2 × (2a + (n − 1)d)
- = 20/2 × (2 × 18 + 19 × 3)
- = 930
6.Find the sum of the first 6 terms of the geometric sequence 1, 2, 4, 8, …
Answer: 63
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (26 − 1) ÷ (2 − 1)
- = 63
7.Find the 6th term of the geometric sequence 1, 4, 16, 64, …
Answer: 1024
- a = 1, r = 4
- T6 = 1 × 45 = 1024
8.For the arithmetic sequence 19, 27, 35, 43, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 11
- d = 27 − 19 = 8
- Tₙ = a + (n − 1)d = 19 + (n − 1) × 8 = 8n + 11
9.Find the sum of the first 5 terms of the geometric sequence 6, −12, 24, −48, …
Answer: 66
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × ((−2)5 − 1) ÷ (−2 − 1)
- = 66
10.Find the 6th term of the geometric sequence −4, −12, −36, −108, …
Answer: −972
- a = −4, r = 3
- T6 = −4 × 35 = −972
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: