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.Find the sum of the first 26 terms of the arithmetic sequence 6, 8, 10, 12, …
Answer: 806
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 6 + 25 × 2)
- = 806
2.Find the sum of the first 9 terms of the arithmetic sequence −6, −10, −14, −18, …
Answer: −198
- Sₙ = n/2 × (2a + (n − 1)d)
- = 9/2 × (2 × −6 + 8 × −4)
- = −198
3.For the arithmetic sequence 18, 19, 20, 21, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 17
- d = 19 − 18 = 1
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 1 = n + 17
4.Find the sum of the first 7 terms of the geometric sequence −4, −8, −16, −32, …
Answer: −508
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (27 − 1) ÷ (2 − 1)
- = −508
5.Find the sum of the first 6 terms of the geometric sequence 1, 5, 25, 125, …
Answer: 3906
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (56 − 1) ÷ (5 − 1)
- = 3906
6.For the geometric sequence −5, −15, −45, −135, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −5 × 3n − 1
- r = −15 ÷ (−5) = 3
7.Find the sum of the first 5 terms of the geometric sequence −2, −6, −18, −54, …
Answer: −242
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −2 × (35 − 1) ÷ (3 − 1)
- = −242
8.Find the 30th term of the arithmetic sequence −3, 4, 11, 18, …
Answer: 200
- a = −3, d = 7
- T30 = −3 + 29 × 7 = 200
9.Find the sum of the first 7 terms of the geometric sequence −1, −5, −25, −125, …
Answer: −19531
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (57 − 1) ÷ (5 − 1)
- = −19531
10.For the arithmetic sequence 6, 8, 10, 12, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 4
- d = 8 − 6 = 2
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 2 = 2n + 4
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.
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