Year 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 11 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Sequences & SeriesYear 11 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the 9th term of the arithmetic sequence −1, −5, −9, −13, …
Answer: −33
- a = −1, d = −4
- T9 = −1 + 8 × −4 = −33
2.Find the sum of the first 5 terms of the geometric sequence 8, 24, 72, 216, …
Answer: 968
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (35 − 1) ÷ (3 − 1)
- = 968
3.Find the sum of the first 29 terms of the arithmetic sequence 12, 16, 20, 24, …
Answer: 1972
- Sₙ = n/2 × (2a + (n − 1)d)
- = 29/2 × (2 × 12 + 28 × 4)
- = 1972
4.Find the 6th term of the geometric sequence 7, 14, 28, 56, …
Answer: 224
- a = 7, r = 2
- T6 = 7 × 25 = 224
5.Find the sum of the first 8 terms of the geometric sequence −1, −5, −25, −125, …
Answer: −97656
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (58 − 1) ÷ (5 − 1)
- = −97656
6.For the geometric sequence 5, 15, 45, 135, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 5 × 3n − 1
- r = 15 ÷ 5 = 3
7.Find the 26th term of the arithmetic sequence 5, 6, 7, 8, …
Answer: 30
- a = 5, d = 1
- T26 = 5 + 25 × 1 = 30
8.Find the sum of the first 12 terms of the arithmetic sequence 5, 10, 15, 20, …
Answer: 390
- Sₙ = n/2 × (2a + (n − 1)d)
- = 12/2 × (2 × 5 + 11 × 5)
- = 390
9.For the geometric sequence 3, 12, 48, 192, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 3 × 4n − 1
- r = 12 ÷ 3 = 4
10.Find the sum of the first 5 terms of the geometric sequence 2, 10, 50, 250, …
Answer: 1562
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (55 − 1) ÷ (5 − 1)
- = 1562
Marking tips
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