Year 10 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 10 sequences & series worksheet.
Success TutoringWorksheetsAnswer sheetYear 10 · Mathematics · Sequences & SeriesYear 10 Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 11 terms of the arithmetic sequence −9, −4, 1, 6, …
Answer: 176
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × −9 + 10 × 5)
- = 176
2.Find the 6th term of the geometric sequence 2, 6, 18, 54, …
Answer: 486
- a = 2, r = 3
- T6 = 2 × 35 = 486
3.Find the 18th term of the arithmetic sequence 1, −1, −3, −5, …
Answer: −33
- a = 1, d = −2
- T18 = 1 + 17 × −2 = −33
4.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
5.Find the sum of the first 7 terms of the geometric sequence 1, 4, 16, 64, …
Answer: 5461
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (47 − 1) ÷ (4 − 1)
- = 5461
6.Find the sum of the first 20 terms of the arithmetic sequence 11, 7, 3, −1, …
Answer: −540
- Sₙ = n/2 × (2a + (n − 1)d)
- = 20/2 × (2 × 11 + 19 × −4)
- = −540
7.For the geometric sequence 3, 15, 75, 375, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 3 × 5n − 1
- r = 15 ÷ 3 = 5
8.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
9.Find the 6th term of the geometric sequence 7, 21, 63, 189, …
Answer: 1701
- a = 7, r = 3
- T6 = 7 × 35 = 1701
10.Find the sum of the first 7 terms of the geometric sequence 2, 10, 50, 250, …
Answer: 39062
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (57 − 1) ÷ (5 − 1)
- = 39062
Marking tips
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