12th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the arithmetic sequence −6, −8, −10, −12, …, write the common difference and the rule for the nth term.
Answer: d = −2; Tₙ = −2n − 4
- d = −8 − (−6) = −2
- Tₙ = a + (n − 1)d = −6 + (n − 1) × −2 = −2n − 4
2.Find the 6th term of the geometric sequence 1, 4, 16, 64, …
Answer: 1024
- a = 1, r = 4
- T6 = 1 × 45 = 1024
3.Find the sum of the first 9 terms of the geometric sequence −3, −9, −27, −81, …
Answer: −29523
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (39 − 1) ÷ (3 − 1)
- = −29523
4.For the geometric sequence −2, −6, −18, −54, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −2 × 3n − 1
- r = −6 ÷ (−2) = 3
5.Find the sum of the first 30 terms of the arithmetic sequence −3, −4, −5, −6, …
Answer: −525
- Sₙ = n/2 × (2a + (n − 1)d)
- = 30/2 × (2 × −3 + 29 × −1)
- = −525
6.Find the 25th term of the arithmetic sequence −8, −13, −18, −23, …
Answer: −128
- a = −8, d = −5
- T25 = −8 + 24 × −5 = −128
7.Find the sum of the first 9 terms of the geometric sequence −2, −8, −32, −128, …
Answer: −174762
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −2 × (49 − 1) ÷ (4 − 1)
- = −174762
8.Find the 18th term of the arithmetic sequence −6, −1, 4, 9, …
Answer: 79
- a = −6, d = 5
- T18 = −6 + 17 × 5 = 79
9.For the arithmetic sequence 18, 27, 36, 45, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 9
- d = 27 − 18 = 9
- Tₙ = a + (n − 1)d = 18 + (n − 1) × 9 = 9n + 9
10.Find the 5th term of the geometric sequence 4, 20, 100, 500, …
Answer: 2500
- a = 4, r = 5
- T5 = 4 × 54 = 2500
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