Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 4, 3, 2, 1, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 5
- d = 3 − 4 = −1
- Tₙ = a + (n − 1)d = 4 + (n − 1) × −1 = −n + 5
2.For the geometric sequence −3, −6, −12, −24, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −3 × 2n − 1
- r = −6 ÷ (−3) = 2
3.Find the sum of the first 9 terms of the geometric sequence 6, 18, 54, 162, …
Answer: 59046
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (39 − 1) ÷ (3 − 1)
- = 59046
4.Find the sum of the first 14 terms of the arithmetic sequence 15, 9, 3, −3, …
Answer: −336
- Sₙ = n/2 × (2a + (n − 1)d)
- = 14/2 × (2 × 15 + 13 × −6)
- = −336
5.Find the sum of the first 15 terms of the arithmetic sequence 17, 26, 35, 44, …
Answer: 1200
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × 17 + 14 × 9)
- = 1200
6.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
7.For the geometric sequence −4, −8, −16, −32, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −4 × 2n − 1
- r = −8 ÷ (−4) = 2
8.Find the sum of the first 28 terms of the arithmetic sequence 5, 11, 17, 23, …
Answer: 2408
- Sₙ = n/2 × (2a + (n − 1)d)
- = 28/2 × (2 × 5 + 27 × 6)
- = 2408
9.Find the sum of the first 27 terms of the arithmetic sequence 2, 10, 18, 26, …
Answer: 2862
- Sₙ = n/2 × (2a + (n − 1)d)
- = 27/2 × (2 × 2 + 26 × 8)
- = 2862
10.Find the sum of the first 6 terms of the geometric sequence −3, 6, −12, 24, …
Answer: 63
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × ((−2)6 − 1) ÷ (−2 − 1)
- = 63
Marking tips
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