Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 1 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 20, 14, 8, 2, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 26
- d = 14 − 20 = −6
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −6 = −6n + 26
2.Find the 8th term of the arithmetic sequence 13, 12, 11, 10, …
Answer: 6
- a = 13, d = −1
- T8 = 13 + 7 × −1 = 6
3.Find the 15th term of the arithmetic sequence 16, 19, 22, 25, …
Answer: 58
- a = 16, d = 3
- T15 = 16 + 14 × 3 = 58
4.Find the 16th term of the arithmetic sequence −4, −3, −2, −1, …
Answer: 11
- a = −4, d = 1
- T16 = −4 + 15 × 1 = 11
5.For the arithmetic sequence 8, 3, −2, −7, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 13
- d = 3 − 8 = −5
- Tₙ = a + (n − 1)d = 8 + (n − 1) × −5 = −5n + 13
6.Find the 8th term of the arithmetic sequence 13, 16, 19, 22, …
Answer: 34
- a = 13, d = 3
- T8 = 13 + 7 × 3 = 34
7.For the arithmetic sequence 17, 20, 23, 26, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 14
- d = 20 − 17 = 3
- Tₙ = a + (n − 1)d = 17 + (n − 1) × 3 = 3n + 14
8.For the arithmetic sequence −8, −7, −6, −5, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n − 9
- d = −7 − (−8) = 1
- Tₙ = a + (n − 1)d = −8 + (n − 1) × 1 = n − 9
9.Find the 18th term of the arithmetic sequence −8, −12, −16, −20, …
Answer: −76
- a = −8, d = −4
- T18 = −8 + 17 × −4 = −76
10.For the arithmetic sequence 15, 23, 31, 39, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 7
- d = 23 − 15 = 8
- Tₙ = a + (n − 1)d = 15 + (n − 1) × 8 = 8n + 7
Marking tips
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