12th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — 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 2 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 18th term of the arithmetic sequence 13, 16, 19, 22, …
Answer: 64
- a = 13, d = 3
- T18 = 13 + 17 × 3 = 64
2.Find the sum of the first 13 terms of the arithmetic sequence 5, 9, 13, 17, …
Answer: 377
- Sₙ = n/2 × (2a + (n − 1)d)
- = 13/2 × (2 × 5 + 12 × 4)
- = 377
3.Find the 7th term of the geometric sequence 8, 16, 32, 64, …
Answer: 512
- a = 8, r = 2
- T7 = 8 × 26 = 512
4.Find the sum of the first 7 terms of the geometric sequence 1, 5, 25, 125, …
Answer: 19531
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (57 − 1) ÷ (5 − 1)
- = 19531
5.For the arithmetic sequence 20, 14, 8, 2, …, write the common difference and the rule for the nth term.
Answer: d = −6; Tₙ = −6n + 26
- d = 14 − 20 = −6
- Tₙ = a + (n − 1)d = 20 + (n − 1) × −6 = −6n + 26
6.Find the 17th term of the arithmetic sequence 13, 22, 31, 40, …
Answer: 157
- a = 13, d = 9
- T17 = 13 + 16 × 9 = 157
7.For the geometric sequence 7, 14, 28, 56, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 7 × 2n − 1
- r = 14 ÷ 7 = 2
8.For the arithmetic sequence 11, 8, 5, 2, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 14
- d = 8 − 11 = −3
- Tₙ = a + (n − 1)d = 11 + (n − 1) × −3 = −3n + 14
9.For the arithmetic sequence −3, −4, −5, −6, …, write the common difference and the rule for the nth term.
Answer: d = −1; Tₙ = −n − 2
- d = −4 − (−3) = −1
- Tₙ = a + (n − 1)d = −3 + (n − 1) × −1 = −n − 2
10.For the arithmetic sequence −4, 2, 8, 14, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 10
- d = 2 − (−4) = 6
- Tₙ = a + (n − 1)d = −4 + (n − 1) × 6 = 6n − 10
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