Year 10 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 10 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Sequences & SeriesYear 10 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 9th term of the geometric sequence 5, −10, 20, −40, …
Answer: 1280
- a = 5, r = −2
- T9 = 5 × (−2)8 = 1280
2.Find the 25th term of the arithmetic sequence 9, 8, 7, 6, …
Answer: −15
- a = 9, d = −1
- T25 = 9 + 24 × −1 = −15
3.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
4.For the arithmetic sequence 10, 13, 16, 19, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 7
- d = 13 − 10 = 3
- Tₙ = a + (n − 1)d = 10 + (n − 1) × 3 = 3n + 7
5.Find the sum of the first 22 terms of the arithmetic sequence −3, 4, 11, 18, …
Answer: 1551
- Sₙ = n/2 × (2a + (n − 1)d)
- = 22/2 × (2 × −3 + 21 × 7)
- = 1551
6.Find the 14th term of the arithmetic sequence 8, 12, 16, 20, …
Answer: 60
- a = 8, d = 4
- T14 = 8 + 13 × 4 = 60
7.Find the sum of the first 6 terms of the geometric sequence 3, −6, 12, −24, …
Answer: −63
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 3 × ((−2)6 − 1) ÷ (−2 − 1)
- = −63
8.For the geometric sequence 4, −8, 16, −32, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 4 × (−2)n − 1
- r = −8 ÷ 4 = −2
9.Find the 20th term of the arithmetic sequence 7, 3, −1, −5, …
Answer: −69
- a = 7, d = −4
- T20 = 7 + 19 × −4 = −69
10.Find the 9th term of the geometric sequence 3, 9, 27, 81, …
Answer: 19683
- a = 3, r = 3
- T9 = 3 × 38 = 19683
Marking tips
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- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
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