Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 8 terms of the geometric sequence 4, 8, 16, 32, …
Answer: 1020
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 4 × (28 − 1) ÷ (2 − 1)
- = 1020
2.For the arithmetic sequence 17, 12, 7, 2, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 22
- d = 12 − 17 = −5
- Tₙ = a + (n − 1)d = 17 + (n − 1) × −5 = −5n + 22
3.Find the sum of the first 6 terms of the geometric sequence −4, −8, −16, −32, …
Answer: −252
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (26 − 1) ÷ (2 − 1)
- = −252
4.For the arithmetic sequence 4, 10, 16, 22, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 2
- d = 10 − 4 = 6
- Tₙ = a + (n − 1)d = 4 + (n − 1) × 6 = 6n − 2
5.For the geometric sequence −2, −4, −8, −16, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −2 × 2n − 1
- r = −4 ÷ (−2) = 2
6.Find the sum of the first 23 terms of the arithmetic sequence −9, −3, 3, 9, …
Answer: 1311
- Sₙ = n/2 × (2a + (n − 1)d)
- = 23/2 × (2 × −9 + 22 × 6)
- = 1311
7.For the geometric sequence −2, −6, −18, −54, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −2 × 3n − 1
- r = −6 ÷ (−2) = 3
8.Find the 9th term of the geometric sequence 8, 24, 72, 216, …
Answer: 52488
- a = 8, r = 3
- T9 = 8 × 38 = 52488
9.Find the sum of the first 9 terms of the geometric sequence 2, 10, 50, 250, …
Answer: 976562
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (59 − 1) ÷ (5 − 1)
- = 976562
10.Find the 8th term of the geometric sequence 6, 18, 54, 162, …
Answer: 13122
- a = 6, r = 3
- T8 = 6 × 37 = 13122
Marking tips
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