Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 9th term of the geometric sequence 4, 20, 100, 500, …
Answer: 1562500
- a = 4, r = 5
- T9 = 4 × 58 = 1562500
2.Find the sum of the first 17 terms of the arithmetic sequence −3, 0, 3, 6, …
Answer: 357
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × −3 + 16 × 3)
- = 357
3.Find the sum of the first 5 terms of the geometric sequence 5, 20, 80, 320, …
Answer: 1705
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (45 − 1) ÷ (4 − 1)
- = 1705
4.Find the sum of the first 9 terms of the geometric sequence 6, −12, 24, −48, …
Answer: 1026
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × ((−2)9 − 1) ÷ (−2 − 1)
- = 1026
5.Find the sum of the first 13 terms of the arithmetic sequence −2, −5, −8, −11, …
Answer: −260
- Sₙ = n/2 × (2a + (n − 1)d)
- = 13/2 × (2 × −2 + 12 × −3)
- = −260
6.Find the sum of the first 13 terms of the arithmetic sequence 1, 8, 15, 22, …
Answer: 559
- Sₙ = n/2 × (2a + (n − 1)d)
- = 13/2 × (2 × 1 + 12 × 7)
- = 559
7.Find the 8th term of the geometric sequence −3, −9, −27, −81, …
Answer: −6561
- a = −3, r = 3
- T8 = −3 × 37 = −6561
8.Find the sum of the first 18 terms of the arithmetic sequence 18, 21, 24, 27, …
Answer: 783
- Sₙ = n/2 × (2a + (n − 1)d)
- = 18/2 × (2 × 18 + 17 × 3)
- = 783
9.Find the 7th term of the geometric sequence 3, 12, 48, 192, …
Answer: 12288
- a = 3, r = 4
- T7 = 3 × 46 = 12288
10.Find the sum of the first 9 terms of the geometric sequence −4, −12, −36, −108, …
Answer: −39364
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (39 − 1) ÷ (3 − 1)
- = −39364
Marking tips
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