Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence 6, 30, 150, 750, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 6 × 5n − 1
- r = 30 ÷ 6 = 5
2.For the geometric sequence 5, 15, 45, 135, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 5 × 3n − 1
- r = 15 ÷ 5 = 3
3.For the geometric sequence 6, −12, 24, −48, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 6 × (−2)n − 1
- r = −12 ÷ 6 = −2
4.For the geometric sequence −2, −8, −32, −128, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = −2 × 4n − 1
- r = −8 ÷ (−2) = 4
5.Find the sum of the first 5 terms of the geometric sequence 3, 15, 75, 375, …
Answer: 2343
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 3 × (55 − 1) ÷ (5 − 1)
- = 2343
6.For the arithmetic sequence 8, 4, 0, −4, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 12
- d = 4 − 8 = −4
- Tₙ = a + (n − 1)d = 8 + (n − 1) × −4 = −4n + 12
7.Find the 30th term of the arithmetic sequence 10, 19, 28, 37, …
Answer: 271
- a = 10, d = 9
- T30 = 10 + 29 × 9 = 271
8.Find the sum of the first 6 terms of the geometric sequence −3, −15, −75, −375, …
Answer: −11718
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (56 − 1) ÷ (5 − 1)
- = −11718
9.Find the sum of the first 17 terms of the arithmetic sequence 19, 23, 27, 31, …
Answer: 867
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × 19 + 16 × 4)
- = 867
10.For the geometric sequence 3, −6, 12, −24, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 3 × (−2)n − 1
- r = −6 ÷ 3 = −2
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