11th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 1 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 21th term of the arithmetic sequence 6, 11, 16, 21, …
Answer: 106
- a = 6, d = 5
- T21 = 6 + 20 × 5 = 106
2.Find the 28th term of the arithmetic sequence −4, 5, 14, 23, …
Answer: 239
- a = −4, d = 9
- T28 = −4 + 27 × 9 = 239
3.For the arithmetic sequence −5, −2, 1, 4, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n − 8
- d = −2 − (−5) = 3
- Tₙ = a + (n − 1)d = −5 + (n − 1) × 3 = 3n − 8
4.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
5.Find the 30th term of the arithmetic sequence 7, 3, −1, −5, …
Answer: −109
- a = 7, d = −4
- T30 = 7 + 29 × −4 = −109
6.Find the 20th term of the arithmetic sequence −9, −3, 3, 9, …
Answer: 105
- a = −9, d = 6
- T20 = −9 + 19 × 6 = 105
7.For the arithmetic sequence 14, 15, 16, 17, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 13
- d = 15 − 14 = 1
- Tₙ = a + (n − 1)d = 14 + (n − 1) × 1 = n + 13
8.For the arithmetic sequence 1, 7, 13, 19, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 5
- d = 7 − 1 = 6
- Tₙ = a + (n − 1)d = 1 + (n − 1) × 6 = 6n − 5
9.For the arithmetic sequence 19, 20, 21, 22, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 18
- d = 20 − 19 = 1
- Tₙ = a + (n − 1)d = 19 + (n − 1) × 1 = n + 18
10.Find the 24th term of the arithmetic sequence 6, 2, −2, −6, …
Answer: −86
- a = 6, d = −4
- T24 = 6 + 23 × −4 = −86
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