Year 11 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 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 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 6th term of the geometric sequence 8, 16, 32, 64, …
Answer: 256
- a = 8, r = 2
- T6 = 8 × 25 = 256
2.Find the 22th term of the arithmetic sequence 17, 23, 29, 35, …
Answer: 143
- a = 17, d = 6
- T22 = 17 + 21 × 6 = 143
3.Find the sum of the first 7 terms of the geometric sequence 8, 40, 200, 1000, …
Answer: 156248
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (57 − 1) ÷ (5 − 1)
- = 156248
4.For the arithmetic sequence 6, 1, −4, −9, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 11
- d = 1 − 6 = −5
- Tₙ = a + (n − 1)d = 6 + (n − 1) × −5 = −5n + 11
5.Find the sum of the first 12 terms of the arithmetic sequence 1, −1, −3, −5, …
Answer: −120
- Sₙ = n/2 × (2a + (n − 1)d)
- = 12/2 × (2 × 1 + 11 × −2)
- = −120
6.For the arithmetic sequence 7, 8, 9, 10, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 6
- d = 8 − 7 = 1
- Tₙ = a + (n − 1)d = 7 + (n − 1) × 1 = n + 6
7.Find the sum of the first 17 terms of the arithmetic sequence −3, −5, −7, −9, …
Answer: −323
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × −3 + 16 × −2)
- = −323
8.Find the sum of the first 27 terms of the arithmetic sequence 15, 10, 5, 0, …
Answer: −1350
- Sₙ = n/2 × (2a + (n − 1)d)
- = 27/2 × (2 × 15 + 26 × −5)
- = −1350
9.Find the 18th term of the arithmetic sequence −3, −8, −13, −18, …
Answer: −88
- a = −3, d = −5
- T18 = −3 + 17 × −5 = −88
10.Find the sum of the first 30 terms of the arithmetic sequence 15, 24, 33, 42, …
Answer: 4365
- Sₙ = n/2 × (2a + (n − 1)d)
- = 30/2 × (2 × 15 + 29 × 9)
- = 4365
Marking tips
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