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.Find the 15th term of the arithmetic sequence −9, −1, 7, 15, …
Answer: 103
- a = −9, d = 8
- T15 = −9 + 14 × 8 = 103
2.For the arithmetic sequence 18, 24, 30, 36, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 12
- d = 24 − 18 = 6
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 6 = 6n + 12
3.For the arithmetic sequence 9, 15, 21, 27, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 3
- d = 15 − 9 = 6
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 6 = 6n + 3
4.Find the 23th term of the arithmetic sequence 5, 2, −1, −4, …
Answer: −61
- a = 5, d = −3
- T23 = 5 + 22 × −3 = −61
5.Find the 18th term of the arithmetic sequence −9, 0, 9, 18, …
Answer: 144
- a = −9, d = 9
- T18 = −9 + 17 × 9 = 144
6.Find the 27th term of the arithmetic sequence −10, −8, −6, −4, …
Answer: 42
- a = −10, d = 2
- T27 = −10 + 26 × 2 = 42
7.Find the 30th term of the arithmetic sequence −6, 0, 6, 12, …
Answer: 168
- a = −6, d = 6
- T30 = −6 + 29 × 6 = 168
8.Find the 27th term of the arithmetic sequence 10, 19, 28, 37, …
Answer: 244
- a = 10, d = 9
- T27 = 10 + 26 × 9 = 244
9.For the arithmetic sequence −3, −4, −5, −6, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n − 2
- d = −4 − (−3) = −1
- Tₙ = a + (n − 1)d = −3 + (n − 1) × −1 = −n − 2
10.For the arithmetic sequence −10, −12, −14, −16, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 8
- d = −12 − (−10) = −2
- Tₙ = a + (n − 1)d = −10 + (n − 1) × −2 = −2n − 8
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