Year 10 Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence 5, −10, 20, −40, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 5 × (−2)n − 1
- r = −10 ÷ 5 = −2
2.For the arithmetic sequence 17, 12, 7, 2, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 22
- d = 12 − 17 = −5
- Tₙ = a + (n − 1)d = 17 + (n − 1) × −5 = −5n + 22
3.Find the sum of the first 6 terms of the geometric sequence 5, 15, 45, 135, …
Answer: 1820
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (36 − 1) ÷ (3 − 1)
- = 1820
4.Find the sum of the first 29 terms of the arithmetic sequence 6, 15, 24, 33, …
Answer: 3828
- Sₙ = n/2 × (2a + (n − 1)d)
- = 29/2 × (2 × 6 + 28 × 9)
- = 3828
5.For the geometric sequence 1, −2, 4, −8, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 1 × (−2)n − 1
- r = −2 ÷ 1 = −2
6.For the geometric sequence 2, 4, 8, 16, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 2 × 2n − 1
- r = 4 ÷ 2 = 2
7.Find the sum of the first 8 terms of the geometric sequence −3, −15, −75, −375, …
Answer: −292968
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (58 − 1) ÷ (5 − 1)
- = −292968
8.Find the 6th term of the geometric sequence 8, 32, 128, 512, …
Answer: 8192
- a = 8, r = 4
- T6 = 8 × 45 = 8192
9.For the geometric sequence −2, −10, −50, −250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −2 × 5n − 1
- r = −10 ÷ (−2) = 5
10.Find the 8th term of the arithmetic sequence 0, 4, 8, 12, …
Answer: 28
- a = 0, d = 4
- T8 = 0 + 7 × 4 = 28
Marking tips
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