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 arithmetic sequence 12, 9, 6, 3, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 15
- d = 9 − 12 = −3
- Tₙ = a + (n − 1)d = 12 + (n − 1) × −3 = −3n + 15
2.For the geometric sequence 4, 12, 36, 108, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 4 × 3n − 1
- r = 12 ÷ 4 = 3
3.Find the 8th term of the geometric sequence −1, −3, −9, −27, …
Answer: −2187
- a = −1, r = 3
- T8 = −1 × 37 = −2187
4.Find the sum of the first 21 terms of the arithmetic sequence −9, −12, −15, −18, …
Answer: −819
- Sₙ = n/2 × (2a + (n − 1)d)
- = 21/2 × (2 × −9 + 20 × −3)
- = −819
5.For the arithmetic sequence 19, 26, 33, 40, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n + 12
- d = 26 − 19 = 7
- Tₙ = a + (n − 1)d = 19 + (n − 1) × 7 = 7n + 12
6.For the arithmetic sequence −2, 3, 8, 13, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 7
- d = 3 − (−2) = 5
- Tₙ = a + (n − 1)d = −2 + (n − 1) × 5 = 5n − 7
7.Find the 6th term of the geometric sequence −3, −9, −27, −81, …
Answer: −729
- a = −3, r = 3
- T6 = −3 × 35 = −729
8.Find the sum of the first 7 terms of the geometric sequence −3, −12, −48, −192, …
Answer: −16383
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (47 − 1) ÷ (4 − 1)
- = −16383
9.For the geometric sequence 4, −8, 16, −32, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 4 × (−2)n − 1
- r = −8 ÷ 4 = −2
10.Find the 19th term of the arithmetic sequence 7, 16, 25, 34, …
Answer: 169
- a = 7, d = 9
- T19 = 7 + 18 × 9 = 169
Marking tips
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