12th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the geometric sequence −4, −12, −36, −108, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −4 × 3n − 1
- r = −12 ÷ (−4) = 3
2.Find the 16th term of the arithmetic sequence 0, 8, 16, 24, …
Answer: 120
- a = 0, d = 8
- T16 = 0 + 15 × 8 = 120
3.For the arithmetic sequence 5, 9, 13, 17, …, write the common difference and the rule for the nth term.
Answer: d = 4; Tₙ = 4n + 1
- d = 9 − 5 = 4
- Tₙ = a + (n − 1)d = 5 + (n − 1) × 4 = 4n + 1
4.For the arithmetic sequence 3, 5, 7, 9, …, write the common difference and the rule for the nth term.
Answer: d = 2; Tₙ = 2n + 1
- d = 5 − 3 = 2
- Tₙ = a + (n − 1)d = 3 + (n − 1) × 2 = 2n + 1
5.Find the sum of the first 9 terms of the arithmetic sequence 17, 16, 15, 14, …
Answer: 117
- Sₙ = n/2 × (2a + (n − 1)d)
- = 9/2 × (2 × 17 + 8 × −1)
- = 117
6.Find the 8th term of the arithmetic sequence 4, 10, 16, 22, …
Answer: 46
- a = 4, d = 6
- T8 = 4 + 7 × 6 = 46
7.For the geometric sequence 4, 12, 36, 108, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = 4 × 3n − 1
- r = 12 ÷ 4 = 3
8.Find the sum of the first 5 terms of the geometric sequence 4, 8, 16, 32, …
Answer: 124
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 4 × (25 − 1) ÷ (2 − 1)
- = 124
9.Find the sum of the first 5 terms of the geometric sequence −3, 6, −12, 24, …
Answer: −33
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × ((−2)5 − 1) ÷ (−2 − 1)
- = −33
10.Find the 23th term of the arithmetic sequence 2, 4, 6, 8, …
Answer: 46
- a = 2, d = 2
- T23 = 2 + 22 × 2 = 46
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