Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 12 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & SeriesYear 12 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 22th term of the arithmetic sequence 18, 23, 28, 33, …
Answer: 123
- a = 18, d = 5
- T22 = 18 + 21 × 5 = 123
2.Find the 18th term of the arithmetic sequence −9, −10, −11, −12, …
Answer: −26
- a = −9, d = −1
- T18 = −9 + 17 × −1 = −26
3.Find the 10th term of the arithmetic sequence −4, 0, 4, 8, …
Answer: 32
- a = −4, d = 4
- T10 = −4 + 9 × 4 = 32
4.Find the 22th term of the arithmetic sequence −10, −14, −18, −22, …
Answer: −94
- a = −10, d = −4
- T22 = −10 + 21 × −4 = −94
5.For the arithmetic sequence 5, 9, 13, 17, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 1
- d = 9 − 5 = 4
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 4 = 4n + 1
6.For the arithmetic sequence 9, 7, 5, 3, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 11
- d = 7 − 9 = −2
- Tₙ = a + (n − 1)d = 9 + (n − 1) × −2 = −2n + 11
7.For the arithmetic sequence 19, 18, 17, 16, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 20
- d = 18 − 19 = −1
- Tₙ = a + (n − 1)d = 19 + (n − 1) × −1 = −n + 20
8.Find the 12th term of the arithmetic sequence 9, 17, 25, 33, …
Answer: 97
- a = 9, d = 8
- T12 = 9 + 11 × 8 = 97
9.For the arithmetic sequence 1, 3, 5, 7, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 1
- d = 3 − 1 = 2
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 2 = 2n − 1
10.Find the 15th term of the arithmetic sequence 13, 11, 9, 7, …
Answer: −15
- a = 13, d = −2
- T15 = 13 + 14 × −2 = −15
Marking tips
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