Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 5 terms of the geometric sequence 5, 15, 45, 135, …
Answer: 605
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (35 − 1) ÷ (3 − 1)
- = 605
2.Find the 30th term of the arithmetic sequence 10, 14, 18, 22, …
Answer: 126
- a = 10, d = 4
- T30 = 10 + 29 × 4 = 126
3.Find the 5th term of the geometric sequence 4, −8, 16, −32, …
Answer: 64
- a = 4, r = −2
- T5 = 4 × (−2)4 = 64
4.Find the sum of the first 26 terms of the arithmetic sequence −5, −1, 3, 7, …
Answer: 1170
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × −5 + 25 × 4)
- = 1170
5.For the arithmetic sequence 14, 18, 22, 26, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 10
- d = 18 − 14 = 4
- Tₙ = a + (n − 1)d = 14 + (n − 1) × 4 = 4n + 10
6.For the geometric sequence 7, 21, 63, 189, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 7 × 3n − 1
- r = 21 ÷ 7 = 3
7.Find the 5th term of the geometric sequence −4, −8, −16, −32, …
Answer: −64
- a = −4, r = 2
- T5 = −4 × 24 = −64
8.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
9.Find the sum of the first 8 terms of the geometric sequence −5, −25, −125, −625, …
Answer: −488280
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (58 − 1) ÷ (5 − 1)
- = −488280
10.For the geometric sequence 7, −14, 28, −56, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 7 × (−2)n − 1
- r = −14 ÷ 7 = −2
Marking tips
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