Year 12 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 8th term of the arithmetic sequence 4, 5, 6, 7, …
Answer: 11
- a = 4, d = 1
- T8 = 4 + 7 × 1 = 11
2.Find the 29th term of the arithmetic sequence 13, 21, 29, 37, …
Answer: 237
- a = 13, d = 8
- T29 = 13 + 28 × 8 = 237
3.Find the sum of the first 6 terms of the geometric sequence 4, −8, 16, −32, …
Answer: −84
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 4 × ((−2)6 − 1) ÷ (−2 − 1)
- = −84
4.Find the sum of the first 5 terms of the geometric sequence −5, −25, −125, −625, …
Answer: −3905
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (55 − 1) ÷ (5 − 1)
- = −3905
5.Find the 5th term of the geometric sequence 1, −2, 4, −8, …
Answer: 16
- a = 1, r = −2
- T5 = 1 × (−2)4 = 16
6.Find the sum of the first 13 terms of the arithmetic sequence 7, 9, 11, 13, …
Answer: 247
- Sₙ = n/2 × (2a + (n − 1)d)
- = 13/2 × (2 × 7 + 12 × 2)
- = 247
7.Find the sum of the first 6 terms of the geometric sequence 7, −14, 28, −56, …
Answer: −147
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 7 × ((−2)6 − 1) ÷ (−2 − 1)
- = −147
8.Find the sum of the first 28 terms of the arithmetic sequence 7, 10, 13, 16, …
Answer: 1330
- Sₙ = n/2 × (2a + (n − 1)d)
- = 28/2 × (2 × 7 + 27 × 3)
- = 1330
9.Find the 5th term of the geometric sequence 2, 6, 18, 54, …
Answer: 162
- a = 2, r = 3
- T5 = 2 × 34 = 162
10.For the geometric sequence 4, 8, 16, 32, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 4 × 2n − 1
- r = 8 ÷ 4 = 2
Marking tips
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