Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 5th term of the geometric sequence 2, 6, 18, 54, …
Answer: 162
- a = 2, r = 3
- T5 = 2 × 34 = 162
2.For the arithmetic sequence 13, 21, 29, 37, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 5
- d = 21 − 13 = 8
- Tₙ = a + (n − 1)d = 13 + (n − 1) × 8 = 8n + 5
3.For the geometric sequence −1, 2, −4, 8, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = −1 × (−2)n − 1
- r = 2 ÷ (−1) = −2
4.For the arithmetic sequence 1, 7, 13, 19, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 5
- d = 7 − 1 = 6
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 6 = 6n − 5
5.For the geometric sequence 2, 10, 50, 250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 2 × 5n − 1
- r = 10 ÷ 2 = 5
6.Find the sum of the first 8 terms of the geometric sequence 5, 15, 45, 135, …
Answer: 16400
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (38 − 1) ÷ (3 − 1)
- = 16400
7.For the arithmetic sequence 6, 4, 2, 0, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 8
- d = 4 − 6 = −2
- Tₙ = a + (n − 1)d = 6 + (n − 1) × −2 = −2n + 8
8.Find the 5th term of the geometric sequence −1, 2, −4, 8, …
Answer: −16
- a = −1, r = −2
- T5 = −1 × (−2)4 = −16
9.For the arithmetic sequence 11, 6, 1, −4, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 16
- d = 6 − 11 = −5
- Tₙ = a + (n − 1)d = 11 + (n − 1) × −5 = −5n + 16
10.Find the 12th term of the arithmetic sequence −5, 0, 5, 10, …
Answer: 50
- a = −5, d = 5
- T12 = −5 + 11 × 5 = 50
Marking tips
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