Year 13 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 13 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Sequences & SeriesYear 13 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.Find the sum of the first 9 terms of the geometric sequence 5, 20, 80, 320, …
Answer: 436905
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (49 − 1) ÷ (4 − 1)
- = 436905
2.For the arithmetic sequence 20, 28, 36, 44, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 12
- d = 28 − 20 = 8
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 8 = 8n + 12
3.Find the sum of the first 16 terms of the arithmetic sequence −6, −9, −12, −15, …
Answer: −456
- Sₙ = n/2 × (2a + (n − 1)d)
- = 16/2 × (2 × −6 + 15 × −3)
- = −456
4.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
5.For the arithmetic sequence −6, −1, 4, 9, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 11
- d = −1 − (−6) = 5
- Tₙ = a + (n − 1)d = −6 + (n − 1) × 5 = 5n − 11
6.For the arithmetic sequence 10, 8, 6, 4, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 12
- d = 8 − 10 = −2
- Tₙ = a + (n − 1)d = 10 + (n − 1) × −2 = −2n + 12
7.Find the 5th term of the geometric sequence −3, −9, −27, −81, …
Answer: −243
- a = −3, r = 3
- T5 = −3 × 34 = −243
8.Find the sum of the first 9 terms of the geometric sequence −1, −3, −9, −27, …
Answer: −9841
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (39 − 1) ÷ (3 − 1)
- = −9841
9.Find the sum of the first 25 terms of the arithmetic sequence 3, 10, 17, 24, …
Answer: 2175
- Sₙ = n/2 × (2a + (n − 1)d)
- = 25/2 × (2 × 3 + 24 × 7)
- = 2175
10.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
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.