Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 6, 7, 8, 9, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 5
- d = 7 − 6 = 1
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 1 = n + 5
2.Find the 14th term of the arithmetic sequence −5, 1, 7, 13, …
Answer: 73
- a = −5, d = 6
- T14 = −5 + 13 × 6 = 73
3.For the arithmetic sequence 13, 15, 17, 19, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 11
- d = 15 − 13 = 2
- Tₙ = a + (n − 1)d = 13 + (n − 1) × 2 = 2n + 11
4.For the arithmetic sequence 16, 14, 12, 10, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 18
- d = 14 − 16 = −2
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −2 = −2n + 18
5.Find the 10th term of the arithmetic sequence −8, 1, 10, 19, …
Answer: 73
- a = −8, d = 9
- T10 = −8 + 9 × 9 = 73
6.Find the 17th term of the arithmetic sequence −9, −3, 3, 9, …
Answer: 87
- a = −9, d = 6
- T17 = −9 + 16 × 6 = 87
7.Find the 24th term of the arithmetic sequence 7, 12, 17, 22, …
Answer: 122
- a = 7, d = 5
- T24 = 7 + 23 × 5 = 122
8.Find the 22th term of the arithmetic sequence −9, −12, −15, −18, …
Answer: −72
- a = −9, d = −3
- T22 = −9 + 21 × −3 = −72
9.Find the 16th term of the arithmetic sequence 6, 7, 8, 9, …
Answer: 21
- a = 6, d = 1
- T16 = 6 + 15 × 1 = 21
10.For the arithmetic sequence 12, 13, 14, 15, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 11
- d = 13 − 12 = 1
- Tₙ = a + (n − 1)d = 12 + (n − 1) × 1 = n + 11
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