Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence 7, 2, −3, −8, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 12
- d = 2 − 7 = −5
- Tₙ = a + (n − 1)d = 7 + (n − 1) × −5 = −5n + 12
2.For the geometric sequence −1, −2, −4, −8, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −1 × 2n − 1
- r = −2 ÷ (−1) = 2
3.Find the 5th term of the geometric sequence 6, 18, 54, 162, …
Answer: 486
- a = 6, r = 3
- T5 = 6 × 34 = 486
4.For the geometric sequence 4, 16, 64, 256, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 4 × 4n − 1
- r = 16 ÷ 4 = 4
5.Find the 7th term of the geometric sequence −1, −3, −9, −27, …
Answer: −729
- a = −1, r = 3
- T7 = −1 × 36 = −729
6.Find the sum of the first 28 terms of the arithmetic sequence 7, 10, 13, 16, …
Answer: 1330
- Sₙ = n/2 × (2a + (n − 1)d)
- = 28/2 × (2 × 7 + 27 × 3)
- = 1330
7.Find the sum of the first 6 terms of the geometric sequence 6, 12, 24, 48, …
Answer: 378
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (26 − 1) ÷ (2 − 1)
- = 378
8.Find the 5th term of the geometric sequence −1, −5, −25, −125, …
Answer: −625
- a = −1, r = 5
- T5 = −1 × 54 = −625
9.For the arithmetic sequence 17, 12, 7, 2, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 22
- d = 12 − 17 = −5
- Tₙ = a + (n − 1)d = 17 + (n − 1) × −5 = −5n + 22
10.For the geometric sequence −3, −15, −75, −375, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −3 × 5n − 1
- r = −15 ÷ (−3) = 5
Marking tips
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