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.For the arithmetic sequence 3, −2, −7, −12, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 8
- d = −2 − 3 = −5
- Tₙ = a + (n − 1)d = 3 + (n − 1) × −5 = −5n + 8
2.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
3.For the arithmetic sequence −5, 3, 11, 19, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 13
- d = 3 − (−5) = 8
- Tₙ = a + (n − 1)d = −5 + (n − 1) × 8 = 8n − 13
4.For the arithmetic sequence −5, 0, 5, 10, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 10
- d = 0 − (−5) = 5
- Tₙ = a + (n − 1)d = −5 + (n − 1) × 5 = 5n − 10
5.For the arithmetic sequence 5, 3, 1, −1, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 7
- d = 3 − 5 = −2
- Tₙ = a + (n − 1)d = 5 + (n − 1) × −2 = −2n + 7
6.Find the 24th term of the arithmetic sequence 13, 15, 17, 19, …
Answer: 59
- a = 13, d = 2
- T24 = 13 + 23 × 2 = 59
7.Find the 12th term of the arithmetic sequence −1, 8, 17, 26, …
Answer: 98
- a = −1, d = 9
- T12 = −1 + 11 × 9 = 98
8.Find the 23th term of the arithmetic sequence −5, 3, 11, 19, …
Answer: 171
- a = −5, d = 8
- T23 = −5 + 22 × 8 = 171
9.Find the 25th term of the arithmetic sequence 10, 18, 26, 34, …
Answer: 202
- a = 10, d = 8
- T25 = 10 + 24 × 8 = 202
10.Find the 23th term of the arithmetic sequence −1, 0, 1, 2, …
Answer: 21
- a = −1, d = 1
- T23 = −1 + 22 × 1 = 21
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