10th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the sum of the first 21 terms of the arithmetic sequence 14, 13, 12, 11, …
Answer: 84
- Sₙ = n/2 × (2a + (n − 1)d)
- = 21/2 × (2 × 14 + 20 × −1)
- = 84
2.Find the 5th term of the geometric sequence −3, −9, −27, −81, …
Answer: −243
- a = −3, r = 3
- T5 = −3 × 34 = −243
3.For the geometric sequence 4, 20, 100, 500, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 4 × 5n − 1
- r = 20 ÷ 4 = 5
4.Find the 10th term of the arithmetic sequence 1, 4, 7, 10, …
Answer: 28
- a = 1, d = 3
- T10 = 1 + 9 × 3 = 28
5.Find the 20th term of the arithmetic sequence 15, 12, 9, 6, …
Answer: −42
- a = 15, d = −3
- T20 = 15 + 19 × −3 = −42
6.Find the 6th term of the geometric sequence 2, 6, 18, 54, …
Answer: 486
- a = 2, r = 3
- T6 = 2 × 35 = 486
7.Find the sum of the first 19 terms of the arithmetic sequence 8, 10, 12, 14, …
Answer: 494
- Sₙ = n/2 × (2a + (n − 1)d)
- = 19/2 × (2 × 8 + 18 × 2)
- = 494
8.For the geometric sequence 7, −14, 28, −56, …, write the common ratio and the rule for the nth term.
Answer: r = −2; Tₙ = 7 × (−2)n − 1
- r = −14 ÷ 7 = −2
9.For the arithmetic sequence 13, 8, 3, −2, …, write the common difference and the rule for the nth term.
Answer: d = −5; Tₙ = −5n + 18
- d = 8 − 13 = −5
- Tₙ = a + (n − 1)d = 13 + (n − 1) × −5 = −5n + 18
10.For the geometric sequence 4, 16, 64, 256, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 4 × 4n − 1
- r = 16 ÷ 4 = 4
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