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 11, 10, 9, 8, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 12
- d = 10 − 11 = −1
- Tₙ = a + (n − 1)d = 11 + (n − 1) × −1 = −n + 12
2.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
3.For the arithmetic sequence −7, −1, 5, 11, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 13
- d = −1 − (−7) = 6
- Tₙ = a + (n − 1)d = −7 + (n − 1) × 6 = 6n − 13
4.For the arithmetic sequence 16, 19, 22, 25, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 13
- d = 19 − 16 = 3
- Tₙ = a + (n − 1)d = 16 + (n − 1) × 3 = 3n + 13
5.Find the 19th term of the arithmetic sequence −10, −2, 6, 14, …
Answer: 134
- a = −10, d = 8
- T19 = −10 + 18 × 8 = 134
6.Find the 15th term of the arithmetic sequence 5, 6, 7, 8, …
Answer: 19
- a = 5, d = 1
- T15 = 5 + 14 × 1 = 19
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.Find the 13th term of the arithmetic sequence 13, 9, 5, 1, …
Answer: −35
- a = 13, d = −4
- T13 = 13 + 12 × −4 = −35
9.Find the 16th term of the arithmetic sequence 7, 5, 3, 1, …
Answer: −23
- a = 7, d = −2
- T16 = 7 + 15 × −2 = −23
10.Find the 25th term of the arithmetic sequence 18, 19, 20, 21, …
Answer: 42
- a = 18, d = 1
- T25 = 18 + 24 × 1 = 42
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