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 5th term of the geometric sequence −2, −4, −8, −16, …
Answer: −32
- a = −2, r = 2
- T5 = −2 × 24 = −32
2.Find the 9th term of the geometric sequence 3, 6, 12, 24, …
Answer: 768
- a = 3, r = 2
- T9 = 3 × 28 = 768
3.Find the 5th term of the geometric sequence −3, −9, −27, −81, …
Answer: −243
- a = −3, r = 3
- T5 = −3 × 34 = −243
4.For the arithmetic sequence 18, 14, 10, 6, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 22
- d = 14 − 18 = −4
- Tₙ = a + (n − 1)d = 18 + (n − 1) × −4 = −4n + 22
5.Find the 8th term of the geometric sequence −1, −2, −4, −8, …
Answer: −128
- a = −1, r = 2
- T8 = −1 × 27 = −128
6.Find the sum of the first 7 terms of the geometric sequence −4, −12, −36, −108, …
Answer: −4372
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (37 − 1) ÷ (3 − 1)
- = −4372
7.Find the 9th term of the geometric sequence 4, −8, 16, −32, …
Answer: 1024
- a = 4, r = −2
- T9 = 4 × (−2)8 = 1024
8.Find the sum of the first 9 terms of the geometric sequence −5, −25, −125, −625, …
Answer: −2441405
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (59 − 1) ÷ (5 − 1)
- = −2441405
9.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
10.Find the 8th term of the geometric sequence −2, −4, −8, −16, …
Answer: −256
- a = −2, r = 2
- T8 = −2 × 27 = −256
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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