Year 13 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 13 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Sequences & SeriesYear 13 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence 4, 12, 36, 108, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 4 × 3n − 1
- r = 12 ÷ 4 = 3
2.Find the 9th term of the arithmetic sequence −10, −1, 8, 17, …
Answer: 62
- a = −10, d = 9
- T9 = −10 + 8 × 9 = 62
3.For the arithmetic sequence 8, 16, 24, 32, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n
- d = 16 − 8 = 8
- Tₙ = a + (n − 1)d = 8 + (n − 1) × 8 = 8n
4.For the arithmetic sequence −10, −16, −22, −28, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n − 4
- d = −16 − (−10) = −6
- Tₙ = a + (n − 1)d = −10 + (n − 1) × −6 = −6n − 4
5.Find the 5th term of the geometric sequence 4, −8, 16, −32, …
Answer: 64
- a = 4, r = −2
- T5 = 4 × (−2)4 = 64
6.Find the 10th term of the arithmetic sequence −7, 1, 9, 17, …
Answer: 65
- a = −7, d = 8
- T10 = −7 + 9 × 8 = 65
7.Find the 10th term of the arithmetic sequence 1, 7, 13, 19, …
Answer: 55
- a = 1, d = 6
- T10 = 1 + 9 × 6 = 55
8.For the geometric sequence 7, 28, 112, 448, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 7 × 4n − 1
- r = 28 ÷ 7 = 4
9.For the geometric sequence 6, 18, 54, 162, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 6 × 3n − 1
- r = 18 ÷ 6 = 3
10.Find the sum of the first 7 terms of the geometric sequence −5, −10, −20, −40, …
Answer: −635
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (27 − 1) ÷ (2 − 1)
- = −635
Marking tips
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