Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence −1, 0, 1, 2, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n − 2
- d = 0 − (−1) = 1
- Tₙ = a + (n − 1)d = −1 + (n − 1) × 1 = n − 2
2.Find the sum of the first 17 terms of the arithmetic sequence 10, 12, 14, 16, …
Answer: 442
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × 10 + 16 × 2)
- = 442
3.Find the 7th term of the geometric sequence −5, −10, −20, −40, …
Answer: −320
- a = −5, r = 2
- T7 = −5 × 26 = −320
4.Find the 28th term of the arithmetic sequence 3, 5, 7, 9, …
Answer: 57
- a = 3, d = 2
- T28 = 3 + 27 × 2 = 57
5.For the geometric sequence 6, 18, 54, 162, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 6 × 3n − 1
- r = 18 ÷ 6 = 3
6.Find the 10th term of the arithmetic sequence 10, 16, 22, 28, …
Answer: 64
- a = 10, d = 6
- T10 = 10 + 9 × 6 = 64
7.Find the 10th term of the arithmetic sequence −7, −8, −9, −10, …
Answer: −16
- a = −7, d = −1
- T10 = −7 + 9 × −1 = −16
8.Find the 14th term of the arithmetic sequence −7, −3, 1, 5, …
Answer: 45
- a = −7, d = 4
- T14 = −7 + 13 × 4 = 45
9.Find the sum of the first 15 terms of the arithmetic sequence 18, 25, 32, 39, …
Answer: 1005
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × 18 + 14 × 7)
- = 1005
10.Find the sum of the first 6 terms of the geometric sequence −3, −12, −48, −192, …
Answer: −4095
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (46 − 1) ÷ (4 − 1)
- = −4095
Marking tips
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