10th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 10th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Sequences & Series10th 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 −7, −3, 1, 5, …
Answer: 65
- a = −7, d = 4
- T19 = −7 + 18 × 4 = 65
2.Find the 10th term of the arithmetic sequence 12, 17, 22, 27, …
Answer: 57
- a = 12, d = 5
- T10 = 12 + 9 × 5 = 57
3.For the arithmetic sequence −1, −2, −3, −4, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n
- d = −2 − (−1) = −1
- Tₙ = a + (n − 1)d = −1 + (n − 1) × −1 = −n
4.Find the 20th term of the arithmetic sequence −5, 0, 5, 10, …
Answer: 90
- a = −5, d = 5
- T20 = −5 + 19 × 5 = 90
5.For the arithmetic sequence 3, 8, 13, 18, …, write the common difference and the rule for the nth term.
Answer: d = 5; Tₙ = 5n − 2
- d = 8 − 3 = 5
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 5 = 5n − 2
6.For the arithmetic sequence 17, 18, 19, 20, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 16
- d = 18 − 17 = 1
- Tₙ = a + (n − 1)d = 17 + (n − 1) × 1 = n + 16
7.Find the 29th term of the arithmetic sequence 13, 7, 1, −5, …
Answer: −155
- a = 13, d = −6
- T29 = 13 + 28 × −6 = −155
8.For the arithmetic sequence −3, 0, 3, 6, …, write the common difference and the rule for the nth term.
Answer: d = 3; Tₙ = 3n − 6
- d = 0 − (−3) = 3
- Tₙ = a + (n − 1)d = −3 + (n − 1) × 3 = 3n − 6
9.For the arithmetic sequence 11, 17, 23, 29, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n + 5
- d = 17 − 11 = 6
- Tₙ = a + (n − 1)d = 11 + (n − 1) × 6 = 6n + 5
10.For the arithmetic sequence −3, 6, 15, 24, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 12
- d = 6 − (−3) = 9
- Tₙ = a + (n − 1)d = −3 + (n − 1) × 9 = 9n − 12
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