10th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the geometric sequence 3, 15, 75, 375, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 3 × 5n − 1
- r = 15 ÷ 3 = 5
2.Find the sum of the first 16 terms of the arithmetic sequence 4, 7, 10, 13, …
Answer: 424
- Sₙ = n/2 × (2a + (n − 1)d)
- = 16/2 × (2 × 4 + 15 × 3)
- = 424
3.For the arithmetic sequence 18, 14, 10, 6, …, write the common difference and the rule for the nth term.
Answer: d = −4; Tₙ = −4n + 22
- d = 14 − 18 = −4
- Tₙ = a + (n − 1)d = 18 + (n − 1) × −4 = −4n + 22
4.For the arithmetic sequence 4, 9, 14, 19, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 1
- d = 9 − 4 = 5
- Tₙ = a + (n − 1)d = 4 + (n − 1) × 5 = 5n − 1
5.Find the sum of the first 5 terms of the geometric sequence 8, 16, 32, 64, …
Answer: 248
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (25 − 1) ÷ (2 − 1)
- = 248
6.Find the sum of the first 5 terms of the geometric sequence 6, 12, 24, 48, …
Answer: 186
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (25 − 1) ÷ (2 − 1)
- = 186
7.For the arithmetic sequence 14, 18, 22, 26, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 10
- d = 18 − 14 = 4
- Tₙ = a + (n − 1)d = 14 + (n − 1) × 4 = 4n + 10
8.Find the sum of the first 29 terms of the arithmetic sequence 18, 20, 22, 24, …
Answer: 1334
- Sₙ = n/2 × (2a + (n − 1)d)
- = 29/2 × (2 × 18 + 28 × 2)
- = 1334
9.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
10.Find the 7th term of the geometric sequence −1, 2, −4, 8, …
Answer: −64
- a = −1, r = −2
- T7 = −1 × (−2)6 = −64
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