Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 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.Find the sum of the first 5 terms of the geometric sequence −4, 8, −16, 32, …
Answer: −44
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × ((−2)5 − 1) ÷ (−2 − 1)
- = −44
2.Find the 7th term of the geometric sequence −1, −5, −25, −125, …
Answer: −15625
- a = −1, r = 5
- T7 = −1 × 56 = −15625
3.Find the sum of the first 9 terms of the geometric sequence −1, −5, −25, −125, …
Answer: −488281
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (59 − 1) ÷ (5 − 1)
- = −488281
4.Find the sum of the first 8 terms of the arithmetic sequence 7, 6, 5, 4, …
Answer: 28
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × 7 + 7 × −1)
- = 28
5.Find the sum of the first 17 terms of the arithmetic sequence −2, −7, −12, −17, …
Answer: −714
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × −2 + 16 × −5)
- = −714
6.Find the sum of the first 5 terms of the geometric sequence −1, −4, −16, −64, …
Answer: −341
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (45 − 1) ÷ (4 − 1)
- = −341
7.Find the 19th term of the arithmetic sequence −5, −7, −9, −11, …
Answer: −41
- a = −5, d = −2
- T19 = −5 + 18 × −2 = −41
8.For the geometric sequence 3, −6, 12, −24, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 3 × (−2)n − 1
- r = −6 ÷ 3 = −2
9.Find the sum of the first 5 terms of the geometric sequence −5, −15, −45, −135, …
Answer: −605
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (35 − 1) ÷ (3 − 1)
- = −605
10.Find the 24th term of the arithmetic sequence −4, 5, 14, 23, …
Answer: 203
- a = −4, d = 9
- T24 = −4 + 23 × 9 = 203
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.