Year 10 Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 1 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 12th term of the arithmetic sequence 7, 1, −5, −11, …
Answer: −59
- a = 7, d = −6
- T12 = 7 + 11 × −6 = −59
2.For the arithmetic sequence −1, −7, −13, −19, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 5
- d = −7 − (−1) = −6
- Tₙ = a + (n − 1)d = −1 + (n − 1) × −6 = −6n + 5
3.Find the 12th term of the arithmetic sequence 18, 19, 20, 21, …
Answer: 29
- a = 18, d = 1
- T12 = 18 + 11 × 1 = 29
4.Find the 10th term of the arithmetic sequence 10, 4, −2, −8, …
Answer: −44
- a = 10, d = −6
- T10 = 10 + 9 × −6 = −44
5.For the arithmetic sequence 14, 10, 6, 2, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 18
- d = 10 − 14 = −4
- Tₙ = a + (n − 1)d = 14 + (n − 1) × −4 = −4n + 18
6.Find the 30th term of the arithmetic sequence 11, 20, 29, 38, …
Answer: 272
- a = 11, d = 9
- T30 = 11 + 29 × 9 = 272
7.For the arithmetic sequence −9, −10, −11, −12, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n − 8
- d = −10 − (−9) = −1
- Tₙ = a + (n − 1)d = −9 + (n − 1) × −1 = −n − 8
8.For the arithmetic sequence 0, −3, −6, −9, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 3
- d = −3 − 0 = −3
- Tₙ = a + (n − 1)d = 0 + (n − 1) × −3 = −3n + 3
9.Find the 21th term of the arithmetic sequence 8, 6, 4, 2, …
Answer: −32
- a = 8, d = −2
- T21 = 8 + 20 × −2 = −32
10.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
Marking tips
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