Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 6 terms of the geometric sequence −4, 8, −16, 32, …
Answer: 84
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × ((−2)6 − 1) ÷ (−2 − 1)
- = 84
2.For the geometric sequence −2, −6, −18, −54, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −2 × 3n − 1
- r = −6 ÷ (−2) = 3
3.Find the 8th term of the geometric sequence −3, −15, −75, −375, …
Answer: −234375
- a = −3, r = 5
- T8 = −3 × 57 = −234375
4.Find the 7th term of the geometric sequence 5, −10, 20, −40, …
Answer: 320
- a = 5, r = −2
- T7 = 5 × (−2)6 = 320
5.Find the 10th term of the arithmetic sequence −5, 4, 13, 22, …
Answer: 76
- a = −5, d = 9
- T10 = −5 + 9 × 9 = 76
6.Find the sum of the first 7 terms of the geometric sequence 4, 16, 64, 256, …
Answer: 21844
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 4 × (47 − 1) ÷ (4 − 1)
- = 21844
7.Find the sum of the first 5 terms of the geometric sequence 6, 18, 54, 162, …
Answer: 726
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (35 − 1) ÷ (3 − 1)
- = 726
8.Find the 12th term of the arithmetic sequence 15, 16, 17, 18, …
Answer: 26
- a = 15, d = 1
- T12 = 15 + 11 × 1 = 26
9.Find the 6th term of the geometric sequence 2, −4, 8, −16, …
Answer: −64
- a = 2, r = −2
- T6 = 2 × (−2)5 = −64
10.Find the 6th term of the geometric sequence 5, 25, 125, 625, …
Answer: 15625
- a = 5, r = 5
- T6 = 5 × 55 = 15625
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.