Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 0, 6, 12, 18, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 6
- d = 6 − 0 = 6
- Tₙ = a + (n − 1)d = 0 + (n − 1) × 6 = 6n − 6
2.Find the 24th term of the arithmetic sequence 13, 12, 11, 10, …
Answer: −10
- a = 13, d = −1
- T24 = 13 + 23 × −1 = −10
3.For the arithmetic sequence 5, 4, 3, 2, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 6
- d = 4 − 5 = −1
- Tₙ = a + (n − 1)d = 5 + (n − 1) × −1 = −n + 6
4.For the arithmetic sequence 13, 20, 27, 34, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n + 6
- d = 20 − 13 = 7
- Tₙ = a + (n − 1)d = 13 + (n − 1) × 7 = 7n + 6
5.For the arithmetic sequence 13, 19, 25, 31, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 7
- d = 19 − 13 = 6
- Tₙ = a + (n − 1)d = 13 + (n − 1) × 6 = 6n + 7
6.For the arithmetic sequence −6, −9, −12, −15, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n − 3
- d = −9 − (−6) = −3
- Tₙ = a + (n − 1)d = −6 + (n − 1) × −3 = −3n − 3
7.Find the 10th term of the arithmetic sequence 8, 2, −4, −10, …
Answer: −46
- a = 8, d = −6
- T10 = 8 + 9 × −6 = −46
8.Find the 11th term of the arithmetic sequence −2, −7, −12, −17, …
Answer: −52
- a = −2, d = −5
- T11 = −2 + 10 × −5 = −52
9.Find the 23th term of the arithmetic sequence 20, 21, 22, 23, …
Answer: 42
- a = 20, d = 1
- T23 = 20 + 22 × 1 = 42
10.Find the 29th term of the arithmetic sequence 14, 21, 28, 35, …
Answer: 210
- a = 14, d = 7
- T29 = 14 + 28 × 7 = 210
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