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 arithmetic sequence −7, −9, −11, −13, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 5
- d = −9 − (−7) = −2
- Tₙ = a + (n − 1)d = −7 + (n − 1) × −2 = −2n − 5
2.For the arithmetic sequence 9, 11, 13, 15, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 7
- d = 11 − 9 = 2
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 2 = 2n + 7
3.Find the sum of the first 8 terms of the arithmetic sequence 17, 23, 29, 35, …
Answer: 304
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × 17 + 7 × 6)
- = 304
4.For the geometric sequence 7, 35, 175, 875, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 7 × 5n − 1
- r = 35 ÷ 7 = 5
5.Find the 12th term of the arithmetic sequence 14, 10, 6, 2, …
Answer: −30
- a = 14, d = −4
- T12 = 14 + 11 × −4 = −30
6.For the arithmetic sequence −7, −3, 1, 5, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 11
- d = −3 − (−7) = 4
- Tₙ = a + (n − 1)d = −7 + (n − 1) × 4 = 4n − 11
7.For the arithmetic sequence −2, −8, −14, −20, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 4
- d = −8 − (−2) = −6
- Tₙ = a + (n − 1)d = −2 + (n − 1) × −6 = −6n + 4
8.Find the 10th term of the arithmetic sequence −2, −3, −4, −5, …
Answer: −11
- a = −2, d = −1
- T10 = −2 + 9 × −1 = −11
9.Find the 14th term of the arithmetic sequence −4, −1, 2, 5, …
Answer: 35
- a = −4, d = 3
- T14 = −4 + 13 × 3 = 35
10.Find the 7th term of the geometric sequence −4, −16, −64, −256, …
Answer: −16384
- a = −4, r = 4
- T7 = −4 × 46 = −16384
Marking tips
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