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 10th term of the arithmetic sequence 13, 16, 19, 22, …
Answer: 40
- a = 13, d = 3
- T10 = 13 + 9 × 3 = 40
2.For the arithmetic sequence 9, 4, −1, −6, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 14
- d = 4 − 9 = −5
- Tₙ = a + (n − 1)d = 9 + (n − 1) × −5 = −5n + 14
3.For the arithmetic sequence −5, −7, −9, −11, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 3
- d = −7 − (−5) = −2
- Tₙ = a + (n − 1)d = −5 + (n − 1) × −2 = −2n − 3
4.Find the sum of the first 23 terms of the arithmetic sequence 12, 16, 20, 24, …
Answer: 1288
- Sₙ = n/2 × (2a + (n − 1)d)
- = 23/2 × (2 × 12 + 22 × 4)
- = 1288
5.Find the 25th term of the arithmetic sequence 12, 8, 4, 0, …
Answer: −84
- a = 12, d = −4
- T25 = 12 + 24 × −4 = −84
6.Find the sum of the first 7 terms of the geometric sequence 1, 4, 16, 64, …
Answer: 5461
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (47 − 1) ÷ (4 − 1)
- = 5461
7.For the arithmetic sequence 14, 12, 10, 8, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 16
- d = 12 − 14 = −2
- Tₙ = a + (n − 1)d = 14 + (n − 1) × −2 = −2n + 16
8.Find the sum of the first 29 terms of the arithmetic sequence 6, 1, −4, −9, …
Answer: −1856
- Sₙ = n/2 × (2a + (n − 1)d)
- = 29/2 × (2 × 6 + 28 × −5)
- = −1856
9.Find the 23th term of the arithmetic sequence 20, 23, 26, 29, …
Answer: 86
- a = 20, d = 3
- T23 = 20 + 22 × 3 = 86
10.For the geometric sequence 1, 2, 4, 8, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 1 × 2n − 1
- r = 2 ÷ 1 = 2
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