Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — 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 4 — 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 sum of the first 23 terms of the arithmetic sequence −9, −13, −17, −21, …
Answer: −1219
- Sₙ = n/2 × (2a + (n − 1)d)
- = 23/2 × (2 × −9 + 22 × −4)
- = −1219
3.For the arithmetic sequence 1, 3, 5, 7, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n − 1
- d = 3 − 1 = 2
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 2 = 2n − 1
4.Find the 5th term of the geometric sequence 3, 6, 12, 24, …
Answer: 48
- a = 3, r = 2
- T5 = 3 × 24 = 48
5.Find the sum of the first 29 terms of the arithmetic sequence 9, 14, 19, 24, …
Answer: 2291
- Sₙ = n/2 × (2a + (n − 1)d)
- = 29/2 × (2 × 9 + 28 × 5)
- = 2291
6.Find the 8th term of the geometric sequence −3, −6, −12, −24, …
Answer: −384
- a = −3, r = 2
- T8 = −3 × 27 = −384
7.Find the 29th term of the arithmetic sequence 2, 9, 16, 23, …
Answer: 198
- a = 2, d = 7
- T29 = 2 + 28 × 7 = 198
8.For the arithmetic sequence 9, 13, 17, 21, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 5
- d = 13 − 9 = 4
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 4 = 4n + 5
9.Find the sum of the first 15 terms of the arithmetic sequence 16, 11, 6, 1, …
Answer: −285
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × 16 + 14 × −5)
- = −285
10.For the arithmetic sequence −9, −2, 5, 12, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 16
- d = −2 − (−9) = 7
- Tₙ = a + (n − 1)d = −9 + (n − 1) × 7 = 7n − 16
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.
- Celebrate what went well first, then pick one thing to work on next.