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.Find the 9th term of the arithmetic sequence 6, 9, 12, 15, …
Answer: 30
- a = 6, d = 3
- T9 = 6 + 8 × 3 = 30
2.For the arithmetic sequence −2, 0, 2, 4, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 4
- d = 0 − (−2) = 2
- Tₙ = a + (n − 1)d = −2 + (n − 1) × 2 = 2n − 4
3.Find the 30th term of the arithmetic sequence 5, 7, 9, 11, …
Answer: 63
- a = 5, d = 2
- T30 = 5 + 29 × 2 = 63
4.For the arithmetic sequence 5, 12, 19, 26, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 2
- d = 12 − 5 = 7
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 7 = 7n − 2
5.Find the 12th term of the arithmetic sequence 17, 12, 7, 2, …
Answer: −38
- a = 17, d = −5
- T12 = 17 + 11 × −5 = −38
6.For the arithmetic sequence 16, 17, 18, 19, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 15
- d = 17 − 16 = 1
- Tₙ = a + (n − 1)d = 16 + (n − 1) × 1 = n + 15
7.For the arithmetic sequence 18, 19, 20, 21, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 17
- d = 19 − 18 = 1
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 1 = n + 17
8.Find the 18th term of the arithmetic sequence 20, 19, 18, 17, …
Answer: 3
- a = 20, d = −1
- T18 = 20 + 17 × −1 = 3
9.Find the 14th term of the arithmetic sequence −8, −14, −20, −26, …
Answer: −86
- a = −8, d = −6
- T14 = −8 + 13 × −6 = −86
10.For the arithmetic sequence −6, −2, 2, 6, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 10
- d = −2 − (−6) = 4
- Tₙ = a + (n − 1)d = −6 + (n − 1) × 4 = 4n − 10
Marking tips
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