Year 12 Arithmetic and Geometric Sequences Worksheet — Level 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 7th term of the geometric sequence 8, 32, 128, 512, …
Answer: 32768
- a = 8, r = 4
- T7 = 8 × 46 = 32768
2.Find the 5th term of the geometric sequence −2, −8, −32, −128, …
Answer: −512
- a = −2, r = 4
- T5 = −2 × 44 = −512
3.For the arithmetic sequence 12, 14, 16, 18, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 10
- d = 14 − 12 = 2
- Tₙ = a + (n − 1)d = 12 + (n − 1) × 2 = 2n + 10
4.Find the sum of the first 8 terms of the arithmetic sequence −5, 1, 7, 13, …
Answer: 128
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × −5 + 7 × 6)
- = 128
5.Find the sum of the first 30 terms of the arithmetic sequence 0, −3, −6, −9, …
Answer: −1305
- Sₙ = n/2 × (2a + (n − 1)d)
- = 30/2 × (2 × 0 + 29 × −3)
- = −1305
6.Find the sum of the first 7 terms of the geometric sequence 2, −4, 8, −16, …
Answer: 86
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × ((−2)7 − 1) ÷ (−2 − 1)
- = 86
7.Find the sum of the first 26 terms of the arithmetic sequence 9, 4, −1, −6, …
Answer: −1391
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × 9 + 25 × −5)
- = −1391
8.For the arithmetic sequence 3, −1, −5, −9, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 7
- d = −1 − 3 = −4
- Tₙ = a + (n − 1)d = 3 + (n − 1) × −4 = −4n + 7
9.For the arithmetic sequence 6, 8, 10, 12, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 4
- d = 8 − 6 = 2
- Tₙ = a + (n − 1)d = 6 + (n − 1) × 2 = 2n + 4
10.Find the 24th term of the arithmetic sequence 18, 16, 14, 12, …
Answer: −28
- a = 18, d = −2
- T24 = 18 + 23 × −2 = −28
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