12th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 12th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Sequences & Series12th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 19th term of the arithmetic sequence 5, 12, 19, 26, …
Answer: 131
- a = 5, d = 7
- T19 = 5 + 18 × 7 = 131
2.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
3.Find the 17th term of the arithmetic sequence 8, 5, 2, −1, …
Answer: −40
- a = 8, d = −3
- T17 = 8 + 16 × −3 = −40
4.Find the 20th term of the arithmetic sequence 6, 10, 14, 18, …
Answer: 82
- a = 6, d = 4
- T20 = 6 + 19 × 4 = 82
5.Find the 11th term of the arithmetic sequence 11, 13, 15, 17, …
Answer: 31
- a = 11, d = 2
- T11 = 11 + 10 × 2 = 31
6.Find the 24th term of the arithmetic sequence 15, 12, 9, 6, …
Answer: −54
- a = 15, d = −3
- T24 = 15 + 23 × −3 = −54
7.Find the 8th term of the arithmetic sequence 6, 2, −2, −6, …
Answer: −22
- a = 6, d = −4
- T8 = 6 + 7 × −4 = −22
8.For the arithmetic sequence −1, −3, −5, −7, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n + 1
- d = −3 − (−1) = −2
- Tₙ = a + (n − 1)d = −1 + (n − 1) × −2 = −2n + 1
9.Find the 30th term of the arithmetic sequence 20, 24, 28, 32, …
Answer: 136
- a = 20, d = 4
- T30 = 20 + 29 × 4 = 136
10.For the arithmetic sequence 20, 22, 24, 26, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 18
- d = 22 − 20 = 2
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 2 = 2n + 18
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