Year 12 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 2 — 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 8th term of the arithmetic sequence 5, 3, 1, −1, …
Answer: −9
- a = 5, d = −2
- T8 = 5 + 7 × −2 = −9
2.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
3.Find the sum of the first 10 terms of the arithmetic sequence −2, 7, 16, 25, …
Answer: 385
- Sₙ = n/2 × (2a + (n − 1)d)
- = 10/2 × (2 × −2 + 9 × 9)
- = 385
4.Find the 22th term of the arithmetic sequence 5, 9, 13, 17, …
Answer: 89
- a = 5, d = 4
- T22 = 5 + 21 × 4 = 89
5.Find the 10th term of the arithmetic sequence −7, −1, 5, 11, …
Answer: 47
- a = −7, d = 6
- T10 = −7 + 9 × 6 = 47
6.Find the sum of the first 10 terms of the arithmetic sequence −2, 0, 2, 4, …
Answer: 70
- Sₙ = n/2 × (2a + (n − 1)d)
- = 10/2 × (2 × −2 + 9 × 2)
- = 70
7.Find the 7th term of the geometric sequence −3, −15, −75, −375, …
Answer: −46875
- a = −3, r = 5
- T7 = −3 × 56 = −46875
8.For the geometric sequence −2, −10, −50, −250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −2 × 5n − 1
- r = −10 ÷ (−2) = 5
9.For the arithmetic sequence 4, 2, 0, −2, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 6
- d = 2 − 4 = −2
- Tₙ = a + (n − 1)d = 4 + (n − 1) × −2 = −2n + 6
10.Find the sum of the first 24 terms of the arithmetic sequence 17, 20, 23, 26, …
Answer: 1236
- Sₙ = n/2 × (2a + (n − 1)d)
- = 24/2 × (2 × 17 + 23 × 3)
- = 1236
Marking tips
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