11th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the arithmetic sequence 10, 16, 22, 28, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 4
- d = 16 − 10 = 6
- Tₙ = a + (n − 1)d = 10 + (n − 1) × 6 = 6n + 4
2.For the arithmetic sequence 20, 26, 32, 38, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 14
- d = 26 − 20 = 6
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 6 = 6n + 14
3.Find the sum of the first 11 terms of the arithmetic sequence −7, −5, −3, −1, …
Answer: 33
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × −7 + 10 × 2)
- = 33
4.Find the 22th term of the arithmetic sequence −6, −3, 0, 3, …
Answer: 57
- a = −6, d = 3
- T22 = −6 + 21 × 3 = 57
5.Find the sum of the first 22 terms of the arithmetic sequence −7, 0, 7, 14, …
Answer: 1463
- Sₙ = n/2 × (2a + (n − 1)d)
- = 22/2 × (2 × −7 + 21 × 7)
- = 1463
6.Find the 7th term of the geometric sequence −4, −16, −64, −256, …
Answer: −16384
- a = −4, r = 4
- T7 = −4 × 46 = −16384
7.Find the 6th term of the geometric sequence 2, 8, 32, 128, …
Answer: 2048
- a = 2, r = 4
- T6 = 2 × 45 = 2048
8.Find the 15th term of the arithmetic sequence −8, 1, 10, 19, …
Answer: 118
- a = −8, d = 9
- T15 = −8 + 14 × 9 = 118
9.Find the 7th term of the geometric sequence −1, −2, −4, −8, …
Answer: −64
- a = −1, r = 2
- T7 = −1 × 26 = −64
10.For the geometric sequence 1, 5, 25, 125, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 1 × 5n − 1
- r = 5 ÷ 1 = 5
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