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 −5, 2, 9, 16, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 12
- d = 2 − (−5) = 7
- Tₙ = a + (n − 1)d = −5 + (n − 1) × 7 = 7n − 12
2.Find the 25th term of the arithmetic sequence 8, 4, 0, −4, …
Answer: −88
- a = 8, d = −4
- T25 = 8 + 24 × −4 = −88
3.For the arithmetic sequence 20, 27, 34, 41, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n + 13
- d = 27 − 20 = 7
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 7 = 7n + 13
4.Find the 13th term of the arithmetic sequence 20, 16, 12, 8, …
Answer: −28
- a = 20, d = −4
- T13 = 20 + 12 × −4 = −28
5.For the arithmetic sequence 14, 10, 6, 2, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 18
- d = 10 − 14 = −4
- Tₙ = a + (n − 1)d = 14 + (n − 1) × −4 = −4n + 18
6.For the arithmetic sequence 18, 20, 22, 24, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 16
- d = 20 − 18 = 2
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 2 = 2n + 16
7.For the arithmetic sequence 19, 15, 11, 7, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 23
- d = 15 − 19 = −4
- Tₙ = a + (n − 1)d = 19 + (n − 1) × −4 = −4n + 23
8.Find the 27th term of the arithmetic sequence 10, 9, 8, 7, …
Answer: −16
- a = 10, d = −1
- T27 = 10 + 26 × −1 = −16
9.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
10.For the arithmetic sequence 7, 8, 9, 10, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 6
- d = 8 − 7 = 1
- Tₙ = a + (n − 1)d = 7 + (n − 1) × 1 = n + 6
Marking tips
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