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 7th term of the geometric sequence 7, −14, 28, −56, …
Answer: 448
- a = 7, r = −2
- T7 = 7 × (−2)6 = 448
2.For the geometric sequence 2, 6, 18, 54, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 2 × 3n − 1
- r = 6 ÷ 2 = 3
3.Find the 22th term of the arithmetic sequence −1, 6, 13, 20, …
Answer: 146
- a = −1, d = 7
- T22 = −1 + 21 × 7 = 146
4.For the arithmetic sequence 6, 13, 20, 27, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 1
- d = 13 − 6 = 7
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 7 = 7n − 1
5.Find the 18th term of the arithmetic sequence −4, −8, −12, −16, …
Answer: −72
- a = −4, d = −4
- T18 = −4 + 17 × −4 = −72
6.Find the sum of the first 5 terms of the geometric sequence −4, −12, −36, −108, …
Answer: −484
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (35 − 1) ÷ (3 − 1)
- = −484
7.Find the 8th term of the arithmetic sequence 9, 5, 1, −3, …
Answer: −19
- a = 9, d = −4
- T8 = 9 + 7 × −4 = −19
8.Find the 25th term of the arithmetic sequence 5, 8, 11, 14, …
Answer: 77
- a = 5, d = 3
- T25 = 5 + 24 × 3 = 77
9.For the arithmetic sequence −9, −5, −1, 3, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 13
- d = −5 − (−9) = 4
- Tₙ = a + (n − 1)d = −9 + (n − 1) × 4 = 4n − 13
10.Find the 5th term of the geometric sequence −3, −12, −48, −192, …
Answer: −768
- a = −3, r = 4
- T5 = −3 × 44 = −768
Marking tips
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