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 23th term of the arithmetic sequence 10, 13, 16, 19, …
Answer: 76
- a = 10, d = 3
- T23 = 10 + 22 × 3 = 76
2.Find the 25th term of the arithmetic sequence 15, 10, 5, 0, …
Answer: −105
- a = 15, d = −5
- T25 = 15 + 24 × −5 = −105
3.Find the 8th term of the arithmetic sequence 13, 19, 25, 31, …
Answer: 55
- a = 13, d = 6
- T8 = 13 + 7 × 6 = 55
4.For the arithmetic sequence 4, 0, −4, −8, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 8
- d = 0 − 4 = −4
- Tₙ = a + (n − 1)d = 4 + (n − 1) × −4 = −4n + 8
5.Find the 24th term of the arithmetic sequence 18, 21, 24, 27, …
Answer: 87
- a = 18, d = 3
- T24 = 18 + 23 × 3 = 87
6.For the arithmetic sequence 5, −1, −7, −13, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 11
- d = −1 − 5 = −6
- Tₙ = a + (n − 1)d = 5 + (n − 1) × −6 = −6n + 11
7.Find the 17th term of the arithmetic sequence 5, 3, 1, −1, …
Answer: −27
- a = 5, d = −2
- T17 = 5 + 16 × −2 = −27
8.For the arithmetic sequence 13, 8, 3, −2, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 18
- d = 8 − 13 = −5
- Tₙ = a + (n − 1)d = 13 + (n − 1) × −5 = −5n + 18
9.Find the 30th term of the arithmetic sequence 17, 13, 9, 5, …
Answer: −99
- a = 17, d = −4
- T30 = 17 + 29 × −4 = −99
10.Find the 24th term of the arithmetic sequence 13, 10, 7, 4, …
Answer: −56
- a = 13, d = −3
- T24 = 13 + 23 × −3 = −56
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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