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 −8, −2, 4, 10, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 14
- d = −2 − (−8) = 6
- Tₙ = a + (n − 1)d = −8 + (n − 1) × 6 = 6n − 14
2.Find the 22th term of the arithmetic sequence 19, 22, 25, 28, …
Answer: 82
- a = 19, d = 3
- T22 = 19 + 21 × 3 = 82
3.Find the 30th term of the arithmetic sequence 6, 4, 2, 0, …
Answer: −52
- a = 6, d = −2
- T30 = 6 + 29 × −2 = −52
4.For the arithmetic sequence 14, 16, 18, 20, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 12
- d = 16 − 14 = 2
- Tₙ = a + (n − 1)d = 14 + (n − 1) × 2 = 2n + 12
5.Find the 19th term of the arithmetic sequence −9, −6, −3, 0, …
Answer: 45
- a = −9, d = 3
- T19 = −9 + 18 × 3 = 45
6.For the arithmetic sequence 8, 14, 20, 26, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 2
- d = 14 − 8 = 6
- Tₙ = a + (n − 1)d = 8 + (n − 1) × 6 = 6n + 2
7.Find the 15th term of the arithmetic sequence 11, 12, 13, 14, …
Answer: 25
- a = 11, d = 1
- T15 = 11 + 14 × 1 = 25
8.Find the 11th term of the arithmetic sequence 4, 11, 18, 25, …
Answer: 74
- a = 4, d = 7
- T11 = 4 + 10 × 7 = 74
9.Find the 29th term of the arithmetic sequence 2, 4, 6, 8, …
Answer: 58
- a = 2, d = 2
- T29 = 2 + 28 × 2 = 58
10.For the arithmetic sequence −9, −1, 7, 15, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 17
- d = −1 − (−9) = 8
- Tₙ = a + (n − 1)d = −9 + (n − 1) × 8 = 8n − 17
Marking tips
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