Year 13 Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 27th term of the arithmetic sequence 7, 11, 15, 19, …
Answer: 111
- a = 7, d = 4
- T27 = 7 + 26 × 4 = 111
2.Find the 11th term of the arithmetic sequence −6, −8, −10, −12, …
Answer: −26
- a = −6, d = −2
- T11 = −6 + 10 × −2 = −26
3.For the arithmetic sequence 3, 4, 5, 6, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 2
- d = 4 − 3 = 1
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 1 = n + 2
4.For the arithmetic sequence 11, 9, 7, 5, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 13
- d = 9 − 11 = −2
- Tₙ = a + (n − 1)d = 11 + (n − 1) × −2 = −2n + 13
5.Find the 14th term of the arithmetic sequence 18, 14, 10, 6, …
Answer: −34
- a = 18, d = −4
- T14 = 18 + 13 × −4 = −34
6.For the arithmetic sequence 17, 25, 33, 41, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 9
- d = 25 − 17 = 8
- Tₙ = a + (n − 1)d = 17 + (n − 1) × 8 = 8n + 9
7.Find the 20th term of the arithmetic sequence −9, −8, −7, −6, …
Answer: 10
- a = −9, d = 1
- T20 = −9 + 19 × 1 = 10
8.For the arithmetic sequence −4, −3, −2, −1, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n − 5
- d = −3 − (−4) = 1
- Tₙ = a + (n − 1)d = −4 + (n − 1) × 1 = n − 5
9.Find the 22th term of the arithmetic sequence 20, 19, 18, 17, …
Answer: −1
- a = 20, d = −1
- T22 = 20 + 21 × −1 = −1
10.Find the 14th term of the arithmetic sequence 8, 17, 26, 35, …
Answer: 125
- a = 8, d = 9
- T14 = 8 + 13 × 9 = 125
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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