10th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the 10th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Sequences & Series10th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the geometric sequence 5, 20, 80, 320, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 5 × 4n − 1
- r = 20 ÷ 5 = 4
2.Find the sum of the first 11 terms of the arithmetic sequence 11, 10, 9, 8, …
Answer: 66
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × 11 + 10 × −1)
- = 66
3.Find the sum of the first 5 terms of the geometric sequence 8, 40, 200, 1000, …
Answer: 6248
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (55 − 1) ÷ (5 − 1)
- = 6248
4.Find the 22th term of the arithmetic sequence 0, 9, 18, 27, …
Answer: 189
- a = 0, d = 9
- T22 = 0 + 21 × 9 = 189
5.For the arithmetic sequence 13, 9, 5, 1, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 17
- d = 9 − 13 = −4
- Tₙ = a + (n − 1)d = 13 + (n − 1) × −4 = −4n + 17
6.For the arithmetic sequence 8, 5, 2, −1, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 11
- d = 5 − 8 = −3
- Tₙ = a + (n − 1)d = 8 + (n − 1) × −3 = −3n + 11
7.For the geometric sequence −3, −9, −27, −81, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −3 × 3n − 1
- r = −9 ÷ (−3) = 3
8.For the arithmetic sequence 5, 6, 7, 8, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 4
- d = 6 − 5 = 1
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 1 = n + 4
9.Find the sum of the first 8 terms of the arithmetic sequence −1, −3, −5, −7, …
Answer: −64
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × −1 + 7 × −2)
- = −64
10.Find the sum of the first 26 terms of the arithmetic sequence −8, −7, −6, −5, …
Answer: 117
- Sₙ = n/2 × (2a + (n − 1)d)
- = 26/2 × (2 × −8 + 25 × 1)
- = 117
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