Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 17th term of the arithmetic sequence 3, 7, 11, 15, …
Answer: 67
- a = 3, d = 4
- T17 = 3 + 16 × 4 = 67
2.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
3.For the arithmetic sequence 10, 8, 6, 4, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 12
- d = 8 − 10 = −2
- Tₙ = a + (n − 1)d = 10 + (n − 1) × −2 = −2n + 12
4.Find the sum of the first 18 terms of the arithmetic sequence −10, −7, −4, −1, …
Answer: 279
- Sₙ = n/2 × (2a + (n − 1)d)
- = 18/2 × (2 × −10 + 17 × 3)
- = 279
5.Find the 21th term of the arithmetic sequence 14, 8, 2, −4, …
Answer: −106
- a = 14, d = −6
- T21 = 14 + 20 × −6 = −106
6.Find the sum of the first 5 terms of the geometric sequence −1, −2, −4, −8, …
Answer: −31
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (25 − 1) ÷ (2 − 1)
- = −31
7.Find the sum of the first 26 terms of the arithmetic sequence 6, 13, 20, 27, …
Answer: 2431
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 6 + 25 × 7)
- = 2431
8.Find the 9th term of the arithmetic sequence 2, 3, 4, 5, …
Answer: 10
- a = 2, d = 1
- T9 = 2 + 8 × 1 = 10
9.For the arithmetic sequence 3, 8, 13, 18, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 2
- d = 8 − 3 = 5
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 5 = 5n − 2
10.For the arithmetic sequence 20, 18, 16, 14, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 22
- d = 18 − 20 = −2
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −2 = −2n + 22
Marking tips
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