Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 20th term of the arithmetic sequence 9, 16, 23, 30, …
Answer: 142
- a = 9, d = 7
- T20 = 9 + 19 × 7 = 142
2.Find the 5th term of the geometric sequence 8, 16, 32, 64, …
Answer: 128
- a = 8, r = 2
- T5 = 8 × 24 = 128
3.Find the sum of the first 7 terms of the geometric sequence −4, 8, −16, 32, …
Answer: −172
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × ((−2)7 − 1) ÷ (−2 − 1)
- = −172
4.Find the 7th term of the geometric sequence −2, −4, −8, −16, …
Answer: −128
- a = −2, r = 2
- T7 = −2 × 26 = −128
5.For the arithmetic sequence 19, 13, 7, 1, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 25
- d = 13 − 19 = −6
- Tₙ = a + (n − 1)d = 19 + (n − 1) × −6 = −6n + 25
6.Find the sum of the first 15 terms of the arithmetic sequence 12, 8, 4, 0, …
Answer: −240
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × 12 + 14 × −4)
- = −240
7.For the geometric sequence −5, 10, −20, 40, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = −5 × (−2)n − 1
- r = 10 ÷ (−5) = −2
8.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
9.Find the 9th term of the arithmetic sequence 10, 17, 24, 31, …
Answer: 66
- a = 10, d = 7
- T9 = 10 + 8 × 7 = 66
10.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
Marking tips
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