12th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the arithmetic sequence −4, 5, 14, 23, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 13
- d = 5 − (−4) = 9
- Tₙ = a + (n − 1)d = −4 + (n − 1) × 9 = 9n − 13
2.For the arithmetic sequence −6, 1, 8, 15, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 13
- d = 1 − (−6) = 7
- Tₙ = a + (n − 1)d = −6 + (n − 1) × 7 = 7n − 13
3.Find the 27th term of the arithmetic sequence 14, 20, 26, 32, …
Answer: 170
- a = 14, d = 6
- T27 = 14 + 26 × 6 = 170
4.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
5.Find the 10th term of the arithmetic sequence 12, 20, 28, 36, …
Answer: 84
- a = 12, d = 8
- T10 = 12 + 9 × 8 = 84
6.For the arithmetic sequence 12, 14, 16, 18, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 10
- d = 14 − 12 = 2
- Tₙ = a + (n − 1)d = 12 + (n − 1) × 2 = 2n + 10
7.Find the 26th term of the arithmetic sequence 15, 22, 29, 36, …
Answer: 190
- a = 15, d = 7
- T26 = 15 + 25 × 7 = 190
8.Find the 29th term of the arithmetic sequence −1, 8, 17, 26, …
Answer: 251
- a = −1, d = 9
- T29 = −1 + 28 × 9 = 251
9.Find the 16th term of the arithmetic sequence 12, 16, 20, 24, …
Answer: 72
- a = 12, d = 4
- T16 = 12 + 15 × 4 = 72
10.For the arithmetic sequence −5, −6, −7, −8, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n − 4
- d = −6 − (−5) = −1
- Tₙ = a + (n − 1)d = −5 + (n − 1) × −1 = −n − 4
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