Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 2, 6, 10, 14, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 2
- d = 6 − 2 = 4
- Tₙ = a + (n − 1)d = 2 + (n − 1) × 4 = 4n − 2
2.Find the 12th term of the arithmetic sequence 1, 6, 11, 16, …
Answer: 56
- a = 1, d = 5
- T12 = 1 + 11 × 5 = 56
3.For the arithmetic sequence 20, 26, 32, 38, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 14
- d = 26 − 20 = 6
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 6 = 6n + 14
4.Find the 20th term of the arithmetic sequence 14, 11, 8, 5, …
Answer: −43
- a = 14, d = −3
- T20 = 14 + 19 × −3 = −43
5.For the arithmetic sequence 2, −2, −6, −10, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 6
- d = −2 − 2 = −4
- Tₙ = a + (n − 1)d = 2 + (n − 1) × −4 = −4n + 6
6.For the arithmetic sequence 18, 14, 10, 6, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 22
- d = 14 − 18 = −4
- Tₙ = a + (n − 1)d = 18 + (n − 1) × −4 = −4n + 22
7.For the arithmetic sequence −7, −4, −1, 2, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n − 10
- d = −4 − (−7) = 3
- Tₙ = a + (n − 1)d = −7 + (n − 1) × 3 = 3n − 10
8.For the arithmetic sequence 1, 3, 5, 7, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 1
- d = 3 − 1 = 2
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 2 = 2n − 1
9.Find the 11th term of the arithmetic sequence 18, 22, 26, 30, …
Answer: 58
- a = 18, d = 4
- T11 = 18 + 10 × 4 = 58
10.For the arithmetic sequence 2, 3, 4, 5, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 1
- d = 3 − 2 = 1
- Tₙ = a + (n − 1)d = 2 + (n − 1) × 1 = n + 1
Marking tips
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