Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 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 2 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the arithmetic sequence −4, −6, −8, −10, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 2
- d = −6 − (−4) = −2
- Tₙ = a + (n − 1)d = −4 + (n − 1) × −2 = −2n − 2
2.Find the 6th term of the geometric sequence −1, −3, −9, −27, …
Answer: −243
- a = −1, r = 3
- T6 = −1 × 35 = −243
3.Find the sum of the first 20 terms of the arithmetic sequence −1, −4, −7, −10, …
Answer: −590
- Sₙ = n/2 × (2a + (n − 1)d)
- = 20/2 × (2 × −1 + 19 × −3)
- = −590
4.Find the sum of the first 17 terms of the arithmetic sequence 7, 14, 21, 28, …
Answer: 1071
- Sₙ = n/2 × (2a + (n − 1)d)
- = 17/2 × (2 × 7 + 16 × 7)
- = 1071
5.Find the 8th term of the arithmetic sequence 2, 5, 8, 11, …
Answer: 23
- a = 2, d = 3
- T8 = 2 + 7 × 3 = 23
6.Find the 18th term of the arithmetic sequence 1, 7, 13, 19, …
Answer: 103
- a = 1, d = 6
- T18 = 1 + 17 × 6 = 103
7.Find the 27th term of the arithmetic sequence −7, −6, −5, −4, …
Answer: 19
- a = −7, d = 1
- T27 = −7 + 26 × 1 = 19
8.Find the sum of the first 7 terms of the geometric sequence 5, 10, 20, 40, …
Answer: 635
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (27 − 1) ÷ (2 − 1)
- = 635
9.For the geometric sequence 8, 24, 72, 216, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 8 × 3n − 1
- r = 24 ÷ 8 = 3
10.Find the sum of the first 6 terms of the geometric sequence 7, 28, 112, 448, …
Answer: 9555
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 7 × (46 − 1) ÷ (4 − 1)
- = 9555
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