Year 13 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 2 — 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 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 7, −14, 28, −56, …
Answer: 77
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 7 × ((−2)5 − 1) ÷ (−2 − 1)
- = 77
2.For the geometric sequence 8, 32, 128, 512, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 8 × 4n − 1
- r = 32 ÷ 8 = 4
3.For the geometric sequence 3, 12, 48, 192, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 3 × 4n − 1
- r = 12 ÷ 3 = 4
4.Find the 15th term of the arithmetic sequence 5, 1, −3, −7, …
Answer: −51
- a = 5, d = −4
- T15 = 5 + 14 × −4 = −51
5.Find the sum of the first 14 terms of the arithmetic sequence −3, −6, −9, −12, …
Answer: −315
- Sₙ = n/2 × (2a + (n − 1)d)
- = 14/2 × (2 × −3 + 13 × −3)
- = −315
6.Find the sum of the first 13 terms of the arithmetic sequence 11, 6, 1, −4, …
Answer: −247
- Sₙ = n/2 × (2a + (n − 1)d)
- = 13/2 × (2 × 11 + 12 × −5)
- = −247
7.For the arithmetic sequence 5, 11, 17, 23, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 1
- d = 11 − 5 = 6
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 6 = 6n − 1
8.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
9.Find the 30th term of the arithmetic sequence 0, 5, 10, 15, …
Answer: 145
- a = 0, d = 5
- T30 = 0 + 29 × 5 = 145
10.For the arithmetic sequence 18, 26, 34, 42, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 10
- d = 26 − 18 = 8
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 8 = 8n + 10
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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