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 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
2.Find the 11th term of the arithmetic sequence 2, 9, 16, 23, …
Answer: 72
- a = 2, d = 7
- T11 = 2 + 10 × 7 = 72
3.For the arithmetic sequence 16, 12, 8, 4, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 20
- d = 12 − 16 = −4
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −4 = −4n + 20
4.For the arithmetic sequence 13, 7, 1, −5, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 19
- d = 7 − 13 = −6
- Tₙ = a + (n − 1)d = 13 + (n − 1) × −6 = −6n + 19
5.For the arithmetic sequence 11, 6, 1, −4, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 16
- d = 6 − 11 = −5
- Tₙ = a + (n − 1)d = 11 + (n − 1) × −5 = −5n + 16
6.Find the 6th term of the geometric sequence 2, −4, 8, −16, …
Answer: −64
- a = 2, r = −2
- T6 = 2 × (−2)5 = −64
7.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
8.For the arithmetic sequence 18, 22, 26, 30, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 14
- d = 22 − 18 = 4
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 4 = 4n + 14
9.Find the 7th term of the geometric sequence 8, 40, 200, 1000, …
Answer: 125000
- a = 8, r = 5
- T7 = 8 × 56 = 125000
10.Find the sum of the first 26 terms of the arithmetic sequence 7, 14, 21, 28, …
Answer: 2457
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 7 + 25 × 7)
- = 2457
Marking tips
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