Year 13 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 13 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Sequences & SeriesYear 13 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 25th term of the arithmetic sequence 0, 7, 14, 21, …
Answer: 168
- a = 0, d = 7
- T25 = 0 + 24 × 7 = 168
2.Find the 23th term of the arithmetic sequence 18, 20, 22, 24, …
Answer: 62
- a = 18, d = 2
- T23 = 18 + 22 × 2 = 62
3.For the arithmetic sequence −7, −2, 3, 8, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 12
- d = −2 − (−7) = 5
- Tₙ = a + (n − 1)d = −7 + (n − 1) × 5 = 5n − 12
4.Find the 23th term of the arithmetic sequence 12, 21, 30, 39, …
Answer: 210
- a = 12, d = 9
- T23 = 12 + 22 × 9 = 210
5.For the arithmetic sequence −7, −3, 1, 5, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 11
- d = −3 − (−7) = 4
- Tₙ = a + (n − 1)d = −7 + (n − 1) × 4 = 4n − 11
6.For the arithmetic sequence 8, 11, 14, 17, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n + 5
- d = 11 − 8 = 3
- Tₙ = a + (n − 1)d = 8 + (n − 1) × 3 = 3n + 5
7.Find the 22th term of the arithmetic sequence −1, 3, 7, 11, …
Answer: 83
- a = −1, d = 4
- T22 = −1 + 21 × 4 = 83
8.For the arithmetic sequence −6, 3, 12, 21, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 15
- d = 3 − (−6) = 9
- Tₙ = a + (n − 1)d = −6 + (n − 1) × 9 = 9n − 15
9.Find the 26th term of the arithmetic sequence 16, 23, 30, 37, …
Answer: 191
- a = 16, d = 7
- T26 = 16 + 25 × 7 = 191
10.Find the 27th term of the arithmetic sequence 2, 7, 12, 17, …
Answer: 132
- a = 2, d = 5
- T27 = 2 + 26 × 5 = 132
Marking tips
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