Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 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.For the arithmetic sequence −6, 1, 8, 15, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 13
- d = 1 − (−6) = 7
- Tₙ = a + (n − 1)d = −6 + (n − 1) × 7 = 7n − 13
2.Find the 24th term of the arithmetic sequence 3, 9, 15, 21, …
Answer: 141
- a = 3, d = 6
- T24 = 3 + 23 × 6 = 141
3.Find the 10th term of the arithmetic sequence 20, 14, 8, 2, …
Answer: −34
- a = 20, d = −6
- T10 = 20 + 9 × −6 = −34
4.For the arithmetic sequence −3, −9, −15, −21, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 3
- d = −9 − (−3) = −6
- Tₙ = a + (n − 1)d = −3 + (n − 1) × −6 = −6n + 3
5.For the arithmetic sequence −10, −14, −18, −22, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n − 6
- d = −14 − (−10) = −4
- Tₙ = a + (n − 1)d = −10 + (n − 1) × −4 = −4n − 6
6.For the arithmetic sequence 2, 8, 14, 20, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 4
- d = 8 − 2 = 6
- Tₙ = a + (n − 1)d = 2 + (n − 1) × 6 = 6n − 4
7.Find the 12th term of the arithmetic sequence 4, 0, −4, −8, …
Answer: −40
- a = 4, d = −4
- T12 = 4 + 11 × −4 = −40
8.For the arithmetic sequence 5, 3, 1, −1, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 7
- d = 3 − 5 = −2
- Tₙ = a + (n − 1)d = 5 + (n − 1) × −2 = −2n + 7
9.Find the 21th term of the arithmetic sequence 14, 15, 16, 17, …
Answer: 34
- a = 14, d = 1
- T21 = 14 + 20 × 1 = 34
10.For the arithmetic sequence 11, 20, 29, 38, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 2
- d = 20 − 11 = 9
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 9 = 9n + 2
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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