Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 6th term of the geometric sequence 8, 16, 32, 64, …
Answer: 256
- a = 8, r = 2
- T6 = 8 × 25 = 256
2.Find the sum of the first 5 terms of the geometric sequence −1, 2, −4, 8, …
Answer: −11
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × ((−2)5 − 1) ÷ (−2 − 1)
- = −11
3.For the arithmetic sequence −7, 2, 11, 20, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 16
- d = 2 − (−7) = 9
- Tₙ = a + (n − 1)d = −7 + (n − 1) × 9 = 9n − 16
4.For the geometric sequence 8, 32, 128, 512, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 8 × 4n − 1
- r = 32 ÷ 8 = 4
5.Find the 29th term of the arithmetic sequence 14, 16, 18, 20, …
Answer: 70
- a = 14, d = 2
- T29 = 14 + 28 × 2 = 70
6.Find the sum of the first 7 terms of the geometric sequence 5, 25, 125, 625, …
Answer: 97655
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (57 − 1) ÷ (5 − 1)
- = 97655
7.For the geometric sequence 2, −4, 8, −16, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 2 × (−2)n − 1
- r = −4 ÷ 2 = −2
8.Find the 8th term of the geometric sequence 1, 3, 9, 27, …
Answer: 2187
- a = 1, r = 3
- T8 = 1 × 37 = 2187
9.Find the sum of the first 8 terms of the geometric sequence 6, 12, 24, 48, …
Answer: 1530
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (28 − 1) ÷ (2 − 1)
- = 1530
10.Find the 14th term of the arithmetic sequence 1, 10, 19, 28, …
Answer: 118
- a = 1, d = 9
- T14 = 1 + 13 × 9 = 118
Marking tips
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