Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 3 — 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 3 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence 4, 20, 100, 500, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 4 × 5n − 1
- r = 20 ÷ 4 = 5
2.Find the 15th term of the arithmetic sequence 13, 21, 29, 37, …
Answer: 125
- a = 13, d = 8
- T15 = 13 + 14 × 8 = 125
3.For the arithmetic sequence 4, 5, 6, 7, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 3
- d = 5 − 4 = 1
- Tₙ = a + (n − 1)d = 4 + (n − 1) × 1 = n + 3
4.Find the 9th term of the geometric sequence −5, −25, −125, −625, …
Answer: −1953125
- a = −5, r = 5
- T9 = −5 × 58 = −1953125
5.Find the sum of the first 7 terms of the geometric sequence 2, 4, 8, 16, …
Answer: 254
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (27 − 1) ÷ (2 − 1)
- = 254
6.Find the sum of the first 23 terms of the arithmetic sequence −7, −3, 1, 5, …
Answer: 851
- Sₙ = n/2 × (2a + (n − 1)d)
- = 23/2 × (2 × −7 + 22 × 4)
- = 851
7.Find the 29th term of the arithmetic sequence 16, 10, 4, −2, …
Answer: −152
- a = 16, d = −6
- T29 = 16 + 28 × −6 = −152
8.Find the 15th term of the arithmetic sequence −1, 1, 3, 5, …
Answer: 27
- a = −1, d = 2
- T15 = −1 + 14 × 2 = 27
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.Find the sum of the first 12 terms of the arithmetic sequence 19, 25, 31, 37, …
Answer: 624
- Sₙ = n/2 × (2a + (n − 1)d)
- = 12/2 × (2 × 19 + 11 × 6)
- = 624
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
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