Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 12 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Sequences & SeriesYear 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence −5, −4, −3, −2, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n − 6
- d = −4 − (−5) = 1
- Tₙ = a + (n − 1)d = −5 + (n − 1) × 1 = n − 6
2.Find the sum of the first 7 terms of the geometric sequence 7, 14, 28, 56, …
Answer: 889
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 7 × (27 − 1) ÷ (2 − 1)
- = 889
3.For the arithmetic sequence −5, −9, −13, −17, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n − 1
- d = −9 − (−5) = −4
- Tₙ = a + (n − 1)d = −5 + (n − 1) × −4 = −4n − 1
4.Find the 26th term of the arithmetic sequence 15, 21, 27, 33, …
Answer: 165
- a = 15, d = 6
- T26 = 15 + 25 × 6 = 165
5.Find the 27th term of the arithmetic sequence 3, 2, 1, 0, …
Answer: −23
- a = 3, d = −1
- T27 = 3 + 26 × −1 = −23
6.Find the sum of the first 10 terms of the arithmetic sequence 11, 20, 29, 38, …
Answer: 515
- Sₙ = n/2 × (2a + (n − 1)d)
- = 10/2 × (2 × 11 + 9 × 9)
- = 515
7.For the arithmetic sequence 15, 13, 11, 9, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 17
- d = 13 − 15 = −2
- Tₙ = a + (n − 1)d = 15 + (n − 1) × −2 = −2n + 17
8.Find the 24th term of the arithmetic sequence −8, 1, 10, 19, …
Answer: 199
- a = −8, d = 9
- T24 = −8 + 23 × 9 = 199
9.Find the sum of the first 6 terms of the geometric sequence 3, 9, 27, 81, …
Answer: 1092
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 3 × (36 − 1) ÷ (3 − 1)
- = 1092
10.Find the 20th term of the arithmetic sequence −6, −4, −2, 0, …
Answer: 32
- a = −6, d = 2
- T20 = −6 + 19 × 2 = 32
Marking tips
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