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.Find the 14th term of the arithmetic sequence 19, 16, 13, 10, …
Answer: −20
- a = 19, d = −3
- T14 = 19 + 13 × −3 = −20
2.Find the sum of the first 26 terms of the arithmetic sequence 2, 6, 10, 14, …
Answer: 1352
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 2 + 25 × 4)
- = 1352
3.Find the sum of the first 24 terms of the arithmetic sequence 6, 0, −6, −12, …
Answer: −1512
- Sₙ = n/2 × (2a + (n − 1)d)
- = 24/2 × (2 × 6 + 23 × −6)
- = −1512
4.Find the 21th term of the arithmetic sequence −10, −6, −2, 2, …
Answer: 70
- a = −10, d = 4
- T21 = −10 + 20 × 4 = 70
5.Find the 19th term of the arithmetic sequence −6, 0, 6, 12, …
Answer: 102
- a = −6, d = 6
- T19 = −6 + 18 × 6 = 102
6.Find the 6th term of the geometric sequence 2, 10, 50, 250, …
Answer: 6250
- a = 2, r = 5
- T6 = 2 × 55 = 6250
7.Find the 7th term of the geometric sequence −2, −10, −50, −250, …
Answer: −31250
- a = −2, r = 5
- T7 = −2 × 56 = −31250
8.Find the sum of the first 20 terms of the arithmetic sequence 5, −1, −7, −13, …
Answer: −1040
- Sₙ = n/2 × (2a + (n − 1)d)
- = 20/2 × (2 × 5 + 19 × −6)
- = −1040
9.For the geometric sequence 6, 18, 54, 162, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 6 × 3n − 1
- r = 18 ÷ 6 = 3
10.Find the sum of the first 15 terms of the arithmetic sequence 2, 3, 4, 5, …
Answer: 135
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × 2 + 14 × 1)
- = 135
Marking tips
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