Year 10 Arithmetic and Geometric Sequences Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.For the geometric sequence 8, −16, 32, −64, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 8 × (−2)n − 1
- r = −16 ÷ 8 = −2
2.Find the 23th term of the arithmetic sequence 13, 16, 19, 22, …
Answer: 79
- a = 13, d = 3
- T23 = 13 + 22 × 3 = 79
3.For the arithmetic sequence 16, 13, 10, 7, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 19
- d = 13 − 16 = −3
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −3 = −3n + 19
4.Find the 5th term of the geometric sequence 5, 25, 125, 625, …
Answer: 3125
- a = 5, r = 5
- T5 = 5 × 54 = 3125
5.For the arithmetic sequence 9, 17, 25, 33, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n + 1
- d = 17 − 9 = 8
- Tₙ = a + (n − 1)d = 9 + (n − 1) × 8 = 8n + 1
6.Find the 7th term of the geometric sequence 5, 15, 45, 135, …
Answer: 3645
- a = 5, r = 3
- T7 = 5 × 36 = 3645
7.For the arithmetic sequence −1, 4, 9, 14, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 6
- d = 4 − (−1) = 5
- Tₙ = a + (n − 1)d = −1 + (n − 1) × 5 = 5n − 6
8.Find the sum of the first 8 terms of the geometric sequence 8, −16, 32, −64, …
Answer: −680
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × ((−2)8 − 1) ÷ (−2 − 1)
- = −680
9.For the geometric sequence 6, −12, 24, −48, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 6 × (−2)n − 1
- r = −12 ÷ 6 = −2
10.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
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