Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 12 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & SeriesYear 12 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 −7, −10, −13, −16, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n − 4
- d = −10 − (−7) = −3
- Tₙ = a + (n − 1)d = −7 + (n − 1) × −3 = −3n − 4
2.For the arithmetic sequence 5, 14, 23, 32, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 4
- d = 14 − 5 = 9
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 9 = 9n − 4
3.Find the 20th term of the arithmetic sequence −5, −2, 1, 4, …
Answer: 52
- a = −5, d = 3
- T20 = −5 + 19 × 3 = 52
4.Find the 20th term of the arithmetic sequence −8, −13, −18, −23, …
Answer: −103
- a = −8, d = −5
- T20 = −8 + 19 × −5 = −103
5.Find the 27th term of the arithmetic sequence 0, −6, −12, −18, …
Answer: −156
- a = 0, d = −6
- T27 = 0 + 26 × −6 = −156
6.For the arithmetic sequence 12, 19, 26, 33, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n + 5
- d = 19 − 12 = 7
- Tₙ = a + (n − 1)d = 12 + (n − 1) × 7 = 7n + 5
7.Find the 11th term of the arithmetic sequence −5, 1, 7, 13, …
Answer: 55
- a = −5, d = 6
- T11 = −5 + 10 × 6 = 55
8.For the arithmetic sequence 11, 16, 21, 26, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 6
- d = 16 − 11 = 5
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 5 = 5n + 6
9.Find the 24th term of the arithmetic sequence 0, 6, 12, 18, …
Answer: 138
- a = 0, d = 6
- T24 = 0 + 23 × 6 = 138
10.For the arithmetic sequence 1, −5, −11, −17, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 7
- d = −5 − 1 = −6
- Tₙ = a + (n − 1)d = 1 + (n − 1) × −6 = −6n + 7
Marking tips
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