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 13th term of the arithmetic sequence 7, 15, 23, 31, …
Answer: 103
- a = 7, d = 8
- T13 = 7 + 12 × 8 = 103
2.For the arithmetic sequence −2, 1, 4, 7, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n − 5
- d = 1 − (−2) = 3
- Tₙ = a + (n − 1)d = −2 + (n − 1) × 3 = 3n − 5
3.For the arithmetic sequence −8, −7, −6, −5, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n − 9
- d = −7 − (−8) = 1
- Tₙ = a + (n − 1)d = −8 + (n − 1) × 1 = n − 9
4.For the arithmetic sequence 17, 23, 29, 35, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 11
- d = 23 − 17 = 6
- Tₙ = a + (n − 1)d = 17 + (n − 1) × 6 = 6n + 11
5.For the arithmetic sequence 9, 6, 3, 0, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 12
- d = 6 − 9 = −3
- Tₙ = a + (n − 1)d = 9 + (n − 1) × −3 = −3n + 12
6.Find the 30th term of the arithmetic sequence 13, 18, 23, 28, …
Answer: 158
- a = 13, d = 5
- T30 = 13 + 29 × 5 = 158
7.For the arithmetic sequence 7, 3, −1, −5, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 11
- d = 3 − 7 = −4
- Tₙ = a + (n − 1)d = 7 + (n − 1) × −4 = −4n + 11
8.For the arithmetic sequence −3, 6, 15, 24, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 12
- d = 6 − (−3) = 9
- Tₙ = a + (n − 1)d = −3 + (n − 1) × 9 = 9n − 12
9.For the arithmetic sequence −1, 1, 3, 5, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 3
- d = 1 − (−1) = 2
- Tₙ = a + (n − 1)d = −1 + (n − 1) × 2 = 2n − 3
10.Find the 10th term of the arithmetic sequence −10, −16, −22, −28, …
Answer: −64
- a = −10, d = −6
- T10 = −10 + 9 × −6 = −64
Marking tips
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