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.Find the 28th term of the arithmetic sequence 16, 22, 28, 34, …
Answer: 178
- a = 16, d = 6
- T28 = 16 + 27 × 6 = 178
2.Find the 20th term of the arithmetic sequence −7, −13, −19, −25, …
Answer: −121
- a = −7, d = −6
- T20 = −7 + 19 × −6 = −121
3.Find the 29th term of the arithmetic sequence 7, 12, 17, 22, …
Answer: 147
- a = 7, d = 5
- T29 = 7 + 28 × 5 = 147
4.For the arithmetic sequence 19, 13, 7, 1, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 25
- d = 13 − 19 = −6
- Tₙ = a + (n − 1)d = 19 + (n − 1) × −6 = −6n + 25
5.Find the 10th term of the arithmetic sequence 3, 11, 19, 27, …
Answer: 75
- a = 3, d = 8
- T10 = 3 + 9 × 8 = 75
6.For the arithmetic sequence 4, 9, 14, 19, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 1
- d = 9 − 4 = 5
- Tₙ = a + (n − 1)d = 4 + (n − 1) × 5 = 5n − 1
7.For the arithmetic sequence −4, 4, 12, 20, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 12
- d = 4 − (−4) = 8
- Tₙ = a + (n − 1)d = −4 + (n − 1) × 8 = 8n − 12
8.Find the 15th term of the arithmetic sequence −3, −7, −11, −15, …
Answer: −59
- a = −3, d = −4
- T15 = −3 + 14 × −4 = −59
9.For the arithmetic sequence −10, −1, 8, 17, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 19
- d = −1 − (−10) = 9
- Tₙ = a + (n − 1)d = −10 + (n − 1) × 9 = 9n − 19
10.Find the 26th term of the arithmetic sequence −8, −11, −14, −17, …
Answer: −83
- a = −8, d = −3
- T26 = −8 + 25 × −3 = −83
Marking tips
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