Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 12 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & SeriesYear 12 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 14th term of the arithmetic sequence 9, 16, 23, 30, …
Answer: 100
- a = 9, d = 7
- T14 = 9 + 13 × 7 = 100
2.Find the 5th term of the geometric sequence −3, 6, −12, 24, …
Answer: −48
- a = −3, r = −2
- T5 = −3 × (−2)4 = −48
3.Find the sum of the first 19 terms of the arithmetic sequence −6, −8, −10, −12, …
Answer: −456
- Sₙ = n/2 × (2a + (n − 1)d)
- = 19/2 × (2 × −6 + 18 × −2)
- = −456
4.Find the sum of the first 7 terms of the geometric sequence −1, 2, −4, 8, …
Answer: −43
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × ((−2)7 − 1) ÷ (−2 − 1)
- = −43
5.Find the sum of the first 25 terms of the arithmetic sequence −8, −1, 6, 13, …
Answer: 1900
- Sₙ = n/2 × (2a + (n − 1)d)
- = 25/2 × (2 × −8 + 24 × 7)
- = 1900
6.Find the sum of the first 14 terms of the arithmetic sequence 13, 9, 5, 1, …
Answer: −182
- Sₙ = n/2 × (2a + (n − 1)d)
- = 14/2 × (2 × 13 + 13 × −4)
- = −182
7.For the arithmetic sequence −9, −3, 3, 9, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 15
- d = −3 − (−9) = 6
- Tₙ = a + (n − 1)d = −9 + (n − 1) × 6 = 6n − 15
8.Find the sum of the first 7 terms of the geometric sequence −1, −3, −9, −27, …
Answer: −1093
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (37 − 1) ÷ (3 − 1)
- = −1093
9.For the geometric sequence −3, −15, −75, −375, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −3 × 5n − 1
- r = −15 ÷ (−3) = 5
10.For the arithmetic sequence −10, −5, 0, 5, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 15
- d = −5 − (−10) = 5
- Tₙ = a + (n − 1)d = −10 + (n − 1) × 5 = 5n − 15
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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