11th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the 11th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Sequences & Series11th 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 2, 10, 50, 250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 2 × 5n − 1
- r = 10 ÷ 2 = 5
2.Find the sum of the first 5 terms of the geometric sequence −4, −12, −36, −108, …
Answer: −484
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −4 × (35 − 1) ÷ (3 − 1)
- = −484
3.For the geometric sequence 6, 12, 24, 48, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 6 × 2n − 1
- r = 12 ÷ 6 = 2
4.Find the sum of the first 10 terms of the arithmetic sequence −4, −9, −14, −19, …
Answer: −265
- Sₙ = n/2 × (2a + (n − 1)d)
- = 10/2 × (2 × −4 + 9 × −5)
- = −265
5.For the arithmetic sequence −5, −1, 3, 7, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n − 9
- d = −1 − (−5) = 4
- Tₙ = a + (n − 1)d = −5 + (n − 1) × 4 = 4n − 9
6.For the geometric sequence 7, 35, 175, 875, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 7 × 5n − 1
- r = 35 ÷ 7 = 5
7.Find the 6th term of the geometric sequence 4, 16, 64, 256, …
Answer: 4096
- a = 4, r = 4
- T6 = 4 × 45 = 4096
8.For the arithmetic sequence −6, −8, −10, −12, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 4
- d = −8 − (−6) = −2
- Tₙ = a + (n − 1)d = −6 + (n − 1) × −2 = −2n − 4
9.For the geometric sequence 1, 2, 4, 8, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 1 × 2n − 1
- r = 2 ÷ 1 = 2
10.For the arithmetic sequence 2, −1, −4, −7, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 5
- d = −1 − 2 = −3
- Tₙ = a + (n − 1)d = 2 + (n − 1) × −3 = −3n + 5
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