Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 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 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.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
2.Find the 9th term of the geometric sequence −4, 8, −16, 32, …
Answer: −1024
- a = −4, r = −2
- T9 = −4 × (−2)8 = −1024
3.Find the sum of the first 7 terms of the geometric sequence −3, −12, −48, −192, …
Answer: −16383
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (47 − 1) ÷ (4 − 1)
- = −16383
4.Find the sum of the first 5 terms of the geometric sequence −1, −4, −16, −64, …
Answer: −341
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (45 − 1) ÷ (4 − 1)
- = −341
5.For the geometric sequence 4, 12, 36, 108, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 4 × 3n − 1
- r = 12 ÷ 4 = 3
6.Find the 5th term of the geometric sequence −5, −25, −125, −625, …
Answer: −3125
- a = −5, r = 5
- T5 = −5 × 54 = −3125
7.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
8.For the geometric sequence 4, 16, 64, 256, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 4 × 4n − 1
- r = 16 ÷ 4 = 4
9.Find the sum of the first 5 terms of the geometric sequence −5, −15, −45, −135, …
Answer: −605
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (35 − 1) ÷ (3 − 1)
- = −605
10.Find the 19th term of the arithmetic sequence 14, 10, 6, 2, …
Answer: −58
- a = 14, d = −4
- T19 = 14 + 18 × −4 = −58
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.
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