Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 9th term of the arithmetic sequence 2, 10, 18, 26, …
Answer: 66
- a = 2, d = 8
- T9 = 2 + 8 × 8 = 66
2.Find the 22th term of the arithmetic sequence 15, 24, 33, 42, …
Answer: 204
- a = 15, d = 9
- T22 = 15 + 21 × 9 = 204
3.For the arithmetic sequence 11, 7, 3, −1, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 15
- d = 7 − 11 = −4
- Tₙ = a + (n − 1)d = 11 + (n − 1) × −4 = −4n + 15
4.For the arithmetic sequence −10, −15, −20, −25, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n − 5
- d = −15 − (−10) = −5
- Tₙ = a + (n − 1)d = −10 + (n − 1) × −5 = −5n − 5
5.Find the 27th term of the arithmetic sequence −10, −11, −12, −13, …
Answer: −36
- a = −10, d = −1
- T27 = −10 + 26 × −1 = −36
6.For the arithmetic sequence 7, 9, 11, 13, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 5
- d = 9 − 7 = 2
- Tₙ = a + (n − 1)d = 7 + (n − 1) × 2 = 2n + 5
7.For the arithmetic sequence 2, 7, 12, 17, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 3
- d = 7 − 2 = 5
- Tₙ = a + (n − 1)d = 2 + (n − 1) × 5 = 5n − 3
8.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
9.Find the 25th term of the arithmetic sequence −8, −6, −4, −2, …
Answer: 40
- a = −8, d = 2
- T25 = −8 + 24 × 2 = 40
10.For the arithmetic sequence 8, 9, 10, 11, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 7
- d = 9 − 8 = 1
- Tₙ = a + (n − 1)d = 8 + (n − 1) × 1 = n + 7
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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