Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence −2, −4, −6, −8, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n
- d = −4 − (−2) = −2
- Tₙ = a + (n − 1)d = −2 + (n − 1) × −2 = −2n
2.Find the 7th term of the geometric sequence 7, −14, 28, −56, …
Answer: 448
- a = 7, r = −2
- T7 = 7 × (−2)6 = 448
3.For the arithmetic sequence 16, 20, 24, 28, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 12
- d = 20 − 16 = 4
- Tₙ = a + (n − 1)d = 16 + (n − 1) × 4 = 4n + 12
4.Find the sum of the first 6 terms of the geometric sequence 8, −16, 32, −64, …
Answer: −168
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × ((−2)6 − 1) ÷ (−2 − 1)
- = −168
5.Find the sum of the first 6 terms of the geometric sequence 2, −4, 8, −16, …
Answer: −42
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × ((−2)6 − 1) ÷ (−2 − 1)
- = −42
6.Find the 7th term of the geometric sequence 5, 20, 80, 320, …
Answer: 20480
- a = 5, r = 4
- T7 = 5 × 46 = 20480
7.For the geometric sequence −1, −2, −4, −8, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −1 × 2n − 1
- r = −2 ÷ (−1) = 2
8.For the geometric sequence −2, −10, −50, −250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −2 × 5n − 1
- r = −10 ÷ (−2) = 5
9.Find the 27th term of the arithmetic sequence 19, 25, 31, 37, …
Answer: 175
- a = 19, d = 6
- T27 = 19 + 26 × 6 = 175
10.Find the 19th term of the arithmetic sequence −3, −8, −13, −18, …
Answer: −93
- a = −3, d = −5
- T19 = −3 + 18 × −5 = −93
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.
Great work. Here's what to try next: