Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 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 2 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 28 terms of the arithmetic sequence −7, −8, −9, −10, …
Answer: −574
- Sₙ = n/2 × (2a + (n − 1)d)
- = 28/2 × (2 × −7 + 27 × −1)
- = −574
2.For the arithmetic sequence 15, 13, 11, 9, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 17
- d = 13 − 15 = −2
- Tₙ = a + (n − 1)d = 15 + (n − 1) × −2 = −2n + 17
3.For the arithmetic sequence 11, 18, 25, 32, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n + 4
- d = 18 − 11 = 7
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 7 = 7n + 4
4.For the geometric sequence −2, −10, −50, −250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −2 × 5n − 1
- r = −10 ÷ (−2) = 5
5.Find the sum of the first 14 terms of the arithmetic sequence −9, −8, −7, −6, …
Answer: −35
- Sₙ = n/2 × (2a + (n − 1)d)
- = 14/2 × (2 × −9 + 13 × 1)
- = −35
6.Find the 24th term of the arithmetic sequence −5, 0, 5, 10, …
Answer: 110
- a = −5, d = 5
- T24 = −5 + 23 × 5 = 110
7.Find the 10th term of the arithmetic sequence 4, 0, −4, −8, …
Answer: −32
- a = 4, d = −4
- T10 = 4 + 9 × −4 = −32
8.For the geometric sequence −5, −25, −125, −625, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −5 × 5n − 1
- r = −25 ÷ (−5) = 5
9.Find the 14th term of the arithmetic sequence −6, −3, 0, 3, …
Answer: 33
- a = −6, d = 3
- T14 = −6 + 13 × 3 = 33
10.Find the sum of the first 6 terms of the geometric sequence 2, 4, 8, 16, …
Answer: 126
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (26 − 1) ÷ (2 − 1)
- = 126
Marking tips
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