Year 12 Arithmetic and Geometric Sequences Worksheet — Level 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 9th term of the arithmetic sequence −4, 3, 10, 17, …
Answer: 52
- a = −4, d = 7
- T9 = −4 + 8 × 7 = 52
2.Find the sum of the first 7 terms of the geometric sequence −1, −2, −4, −8, …
Answer: −127
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (27 − 1) ÷ (2 − 1)
- = −127
3.Find the 9th term of the geometric sequence −3, 6, −12, 24, …
Answer: −768
- a = −3, r = −2
- T9 = −3 × (−2)8 = −768
4.For the geometric sequence −2, 4, −8, 16, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = −2 × (−2)n − 1
- r = 4 ÷ (−2) = −2
5.For the geometric sequence 4, 20, 100, 500, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 4 × 5n − 1
- r = 20 ÷ 4 = 5
6.Find the sum of the first 7 terms of the geometric sequence 4, 20, 100, 500, …
Answer: 78124
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 4 × (57 − 1) ÷ (5 − 1)
- = 78124
7.Find the 13th term of the arithmetic sequence 17, 19, 21, 23, …
Answer: 41
- a = 17, d = 2
- T13 = 17 + 12 × 2 = 41
8.Find the 24th term of the arithmetic sequence 6, 2, −2, −6, …
Answer: −86
- a = 6, d = −4
- T24 = 6 + 23 × −4 = −86
9.Find the sum of the first 5 terms of the geometric sequence 1, 4, 16, 64, …
Answer: 341
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (45 − 1) ÷ (4 − 1)
- = 341
10.Find the 7th term of the geometric sequence 4, 12, 36, 108, …
Answer: 2916
- a = 4, r = 3
- T7 = 4 × 36 = 2916
Marking tips
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