10th Grade Arithmetic and Geometric Sequences Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 11th term of the arithmetic sequence 4, 9, 14, 19, …
Answer: 54
- a = 4, d = 5
- T11 = 4 + 10 × 5 = 54
2.For the arithmetic sequence 16, 13, 10, 7, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 19
- d = 13 − 16 = −3
- Tₙ = a + (n − 1)d = 16 + (n − 1) × −3 = −3n + 19
3.For the arithmetic sequence 19, 18, 17, 16, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n + 20
- d = 18 − 19 = −1
- Tₙ = a + (n − 1)d = 19 + (n − 1) × −1 = −n + 20
4.For the arithmetic sequence 20, 21, 22, 23, …, write the common difference and the rule for the nth term.
Answer: d = 1; Tₙ = n + 19
- d = 21 − 20 = 1
- Tₙ = a + (n − 1)d = 20 + (n − 1) × 1 = n + 19
5.Find the 19th term of the arithmetic sequence 7, 10, 13, 16, …
Answer: 61
- a = 7, d = 3
- T19 = 7 + 18 × 3 = 61
6.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
7.For the arithmetic sequence 4, 11, 18, 25, …, write the common difference and the rule for the nth term.
Answer: d = 7; Tₙ = 7n − 3
- d = 11 − 4 = 7
- Tₙ = a + (n − 1)d = 4 + (n − 1) × 7 = 7n − 3
8.Find the 22th term of the arithmetic sequence 8, 6, 4, 2, …
Answer: −34
- a = 8, d = −2
- T22 = 8 + 21 × −2 = −34
9.Find the 21th term of the arithmetic sequence 4, 6, 8, 10, …
Answer: 44
- a = 4, d = 2
- T21 = 4 + 20 × 2 = 44
10.Find the 26th term of the arithmetic sequence 14, 17, 20, 23, …
Answer: 89
- a = 14, d = 3
- T26 = 14 + 25 × 3 = 89
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