Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 8th term of the arithmetic sequence 0, 5, 10, 15, …
Answer: 35
- a = 0, d = 5
- T8 = 0 + 7 × 5 = 35
2.For the geometric sequence 4, −8, 16, −32, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 4 × (−2)n − 1
- r = −8 ÷ 4 = −2
3.Find the sum of the first 21 terms of the arithmetic sequence 13, 11, 9, 7, …
Answer: −147
- Sₙ = n/2 × (2a + (n − 1)d)
- = 21/2 × (2 × 13 + 20 × −2)
- = −147
4.Find the 14th term of the arithmetic sequence 15, 16, 17, 18, …
Answer: 28
- a = 15, d = 1
- T14 = 15 + 13 × 1 = 28
5.Find the 20th term of the arithmetic sequence −10, −7, −4, −1, …
Answer: 47
- a = −10, d = 3
- T20 = −10 + 19 × 3 = 47
6.Find the 6th term of the geometric sequence 2, −4, 8, −16, …
Answer: −64
- a = 2, r = −2
- T6 = 2 × (−2)5 = −64
7.Find the 6th term of the geometric sequence −2, −6, −18, −54, …
Answer: −486
- a = −2, r = 3
- T6 = −2 × 35 = −486
8.Find the 15th term of the arithmetic sequence 11, 19, 27, 35, …
Answer: 123
- a = 11, d = 8
- T15 = 11 + 14 × 8 = 123
9.Find the 21th term of the arithmetic sequence 2, 3, 4, 5, …
Answer: 22
- a = 2, d = 1
- T21 = 2 + 20 × 1 = 22
10.Find the sum of the first 6 terms of the geometric sequence −2, −6, −18, −54, …
Answer: −728
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −2 × (36 − 1) ÷ (3 − 1)
- = −728
Marking tips
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