10th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 11th term of the arithmetic sequence 6, 5, 4, 3, …
Answer: −4
- a = 6, d = −1
- T11 = 6 + 10 × −1 = −4
2.Find the sum of the first 5 terms of the geometric sequence 6, 30, 150, 750, …
Answer: 4686
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (55 − 1) ÷ (5 − 1)
- = 4686
3.For the geometric sequence 3, 12, 48, 192, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 3 × 4n − 1
- r = 12 ÷ 3 = 4
4.Find the 18th term of the arithmetic sequence 18, 19, 20, 21, …
Answer: 35
- a = 18, d = 1
- T18 = 18 + 17 × 1 = 35
5.Find the 23th term of the arithmetic sequence 10, 12, 14, 16, …
Answer: 54
- a = 10, d = 2
- T23 = 10 + 22 × 2 = 54
6.Find the 20th term of the arithmetic sequence −8, −1, 6, 13, …
Answer: 125
- a = −8, d = 7
- T20 = −8 + 19 × 7 = 125
7.For the geometric sequence 2, 6, 18, 54, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 2 × 3n − 1
- r = 6 ÷ 2 = 3
8.Find the 6th term of the geometric sequence −4, −8, −16, −32, …
Answer: −128
- a = −4, r = 2
- T6 = −4 × 25 = −128
9.For the arithmetic sequence −3, −7, −11, −15, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 1
- d = −7 − (−3) = −4
- Tₙ = a + (n − 1)d = −3 + (n − 1) × −4 = −4n + 1
10.Find the sum of the first 7 terms of the geometric sequence 2, 8, 32, 128, …
Answer: 10922
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (47 − 1) ÷ (4 − 1)
- = 10922
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