Year 11 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 11, 16, 21, 26, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 6
- d = 16 − 11 = 5
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 5 = 5n + 6
2.Find the 16th term of the arithmetic sequence 18, 17, 16, 15, …
Answer: 3
- a = 18, d = −1
- T16 = 18 + 15 × −1 = 3
3.Find the 10th term of the arithmetic sequence 5, 7, 9, 11, …
Answer: 23
- a = 5, d = 2
- T10 = 5 + 9 × 2 = 23
4.Find the 19th term of the arithmetic sequence 6, 5, 4, 3, …
Answer: −12
- a = 6, d = −1
- T19 = 6 + 18 × −1 = −12
5.Find the 18th term of the arithmetic sequence 3, −3, −9, −15, …
Answer: −99
- a = 3, d = −6
- T18 = 3 + 17 × −6 = −99
6.Find the 13th term of the arithmetic sequence 20, 19, 18, 17, …
Answer: 8
- a = 20, d = −1
- T13 = 20 + 12 × −1 = 8
7.Find the 8th term of the arithmetic sequence −2, 3, 8, 13, …
Answer: 33
- a = −2, d = 5
- T8 = −2 + 7 × 5 = 33
8.Find the 13th term of the arithmetic sequence −6, −11, −16, −21, …
Answer: −66
- a = −6, d = −5
- T13 = −6 + 12 × −5 = −66
9.For the arithmetic sequence 20, 17, 14, 11, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 23
- d = 17 − 20 = −3
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −3 = −3n + 23
10.For the arithmetic sequence 18, 23, 28, 33, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n + 13
- d = 23 − 18 = 5
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 5 = 5n + 13
Marking tips
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