Year 12 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 8th term of the arithmetic sequence −8, −5, −2, 1, …
Answer: 13
- a = −8, d = 3
- T8 = −8 + 7 × 3 = 13
2.For the arithmetic sequence −10, −14, −18, −22, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n − 6
- d = −14 − (−10) = −4
- Tₙ = a + (n − 1)d = −10 + (n − 1) × −4 = −4n − 6
3.For the arithmetic sequence 15, 17, 19, 21, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 13
- d = 17 − 15 = 2
- Tₙ = a + (n − 1)d = 15 + (n − 1) × 2 = 2n + 13
4.Find the 28th term of the arithmetic sequence 7, 11, 15, 19, …
Answer: 115
- a = 7, d = 4
- T28 = 7 + 27 × 4 = 115
5.Find the 23th term of the arithmetic sequence −6, −3, 0, 3, …
Answer: 60
- a = −6, d = 3
- T23 = −6 + 22 × 3 = 60
6.For the arithmetic sequence −3, −2, −1, 0, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n − 4
- d = −2 − (−3) = 1
- Tₙ = a + (n − 1)d = −3 + (n − 1) × 1 = n − 4
7.Find the 18th term of the arithmetic sequence 16, 25, 34, 43, …
Answer: 169
- a = 16, d = 9
- T18 = 16 + 17 × 9 = 169
8.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
9.Find the 11th term of the arithmetic sequence 0, −1, −2, −3, …
Answer: −10
- a = 0, d = −1
- T11 = 0 + 10 × −1 = −10
10.Find the 22th term of the arithmetic sequence −2, 5, 12, 19, …
Answer: 145
- a = −2, d = 7
- T22 = −2 + 21 × 7 = 145
Marking tips
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