Year 10 Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your working.
1.Find the sum of the first 28 terms of the arithmetic sequence −7, −11, −15, −19, …
Answer: −1708
- Sₙ = n/2 × (2a + (n − 1)d)
- = 28/2 × (2 × −7 + 27 × −4)
- = −1708
2.For the geometric sequence 1, 4, 16, 64, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 1 × 4n − 1
- r = 4 ÷ 1 = 4
3.Find the 12th term of the arithmetic sequence 20, 17, 14, 11, …
Answer: −13
- a = 20, d = −3
- T12 = 20 + 11 × −3 = −13
4.Find the 22th term of the arithmetic sequence 3, 0, −3, −6, …
Answer: −60
- a = 3, d = −3
- T22 = 3 + 21 × −3 = −60
5.For the arithmetic sequence 19, 14, 9, 4, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 24
- d = 14 − 19 = −5
- Tₙ = a + (n − 1)d = 19 + (n − 1) × −5 = −5n + 24
6.Find the sum of the first 6 terms of the geometric sequence 6, 18, 54, 162, …
Answer: 2184
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (36 − 1) ÷ (3 − 1)
- = 2184
7.Find the sum of the first 14 terms of the arithmetic sequence 16, 22, 28, 34, …
Answer: 770
- Sₙ = n/2 × (2a + (n − 1)d)
- = 14/2 × (2 × 16 + 13 × 6)
- = 770
8.Find the 25th term of the arithmetic sequence −5, 3, 11, 19, …
Answer: 187
- a = −5, d = 8
- T25 = −5 + 24 × 8 = 187
9.For the arithmetic sequence 5, 13, 21, 29, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 3
- d = 13 − 5 = 8
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 8 = 8n − 3
10.Find the sum of the first 7 terms of the geometric sequence 8, −16, 32, −64, …
Answer: 344
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × ((−2)7 − 1) ÷ (−2 − 1)
- = 344
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