Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 2 — 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 2 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 20 terms of the arithmetic sequence 10, 18, 26, 34, …
Answer: 1720
- Sₙ = n/2 × (2a + (n − 1)d)
- = 20/2 × (2 × 10 + 19 × 8)
- = 1720
2.Find the 6th term of the geometric sequence 1, 4, 16, 64, …
Answer: 1024
- a = 1, r = 4
- T6 = 1 × 45 = 1024
3.Find the sum of the first 5 terms of the geometric sequence 2, 8, 32, 128, …
Answer: 682
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (45 − 1) ÷ (4 − 1)
- = 682
4.Find the sum of the first 22 terms of the arithmetic sequence 1, −1, −3, −5, …
Answer: −440
- Sₙ = n/2 × (2a + (n − 1)d)
- = 22/2 × (2 × 1 + 21 × −2)
- = −440
5.Find the 18th term of the arithmetic sequence 15, 17, 19, 21, …
Answer: 49
- a = 15, d = 2
- T18 = 15 + 17 × 2 = 49
6.For the geometric sequence 3, 9, 27, 81, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 3 × 3n − 1
- r = 9 ÷ 3 = 3
7.Find the 17th term of the arithmetic sequence −1, 8, 17, 26, …
Answer: 143
- a = −1, d = 9
- T17 = −1 + 16 × 9 = 143
8.Find the 21th term of the arithmetic sequence 5, 4, 3, 2, …
Answer: −15
- a = 5, d = −1
- T21 = 5 + 20 × −1 = −15
9.Find the sum of the first 19 terms of the arithmetic sequence −3, −1, 1, 3, …
Answer: 285
- Sₙ = n/2 × (2a + (n − 1)d)
- = 19/2 × (2 × −3 + 18 × 2)
- = 285
10.Find the sum of the first 17 terms of the arithmetic sequence 9, 5, 1, −3, …
Answer: −391
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × 9 + 16 × −4)
- = −391
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
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