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 3, 10, 17, 24, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 4
- d = 10 − 3 = 7
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 7 = 7n − 4
2.For the arithmetic sequence −8, −10, −12, −14, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 6
- d = −10 − (−8) = −2
- Tₙ = a + (n − 1)d = −8 + (n − 1) × −2 = −2n − 6
3.For the arithmetic sequence 11, 13, 15, 17, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 9
- d = 13 − 11 = 2
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 2 = 2n + 9
4.Find the 17th term of the arithmetic sequence 2, 7, 12, 17, …
Answer: 82
- a = 2, d = 5
- T17 = 2 + 16 × 5 = 82
5.For the arithmetic sequence 2, −4, −10, −16, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 8
- d = −4 − 2 = −6
- Tₙ = a + (n − 1)d = 2 + (n − 1) × −6 = −6n + 8
6.Find the 22th term of the arithmetic sequence 8, 12, 16, 20, …
Answer: 92
- a = 8, d = 4
- T22 = 8 + 21 × 4 = 92
7.Find the 28th term of the arithmetic sequence 19, 28, 37, 46, …
Answer: 262
- a = 19, d = 9
- T28 = 19 + 27 × 9 = 262
8.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
9.Find the 8th term of the arithmetic sequence −1, 1, 3, 5, …
Answer: 13
- a = −1, d = 2
- T8 = −1 + 7 × 2 = 13
10.For the arithmetic sequence 0, −4, −8, −12, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 4
- d = −4 − 0 = −4
- Tₙ = a + (n − 1)d = 0 + (n − 1) × −4 = −4n + 4
Marking tips
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