12th Grade Arithmetic and Geometric Sequences Worksheet — Level 2 — Practice Set 3 — 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 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.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
2.Find the 24th term of the arithmetic sequence 5, 3, 1, −1, …
Answer: −41
- a = 5, d = −2
- T24 = 5 + 23 × −2 = −41
3.Find the 25th term of the arithmetic sequence −2, 1, 4, 7, …
Answer: 70
- a = −2, d = 3
- T25 = −2 + 24 × 3 = 70
4.Find the sum of the first 5 terms of the geometric sequence −3, −15, −75, −375, …
Answer: −2343
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (55 − 1) ÷ (5 − 1)
- = −2343
5.Find the 28th term of the arithmetic sequence 10, 4, −2, −8, …
Answer: −152
- a = 10, d = −6
- T28 = 10 + 27 × −6 = −152
6.For the arithmetic sequence 13, 10, 7, 4, …, write the common difference and the rule for the nth term.
Answer: d = −3; Tₙ = −3n + 16
- d = 10 − 13 = −3
- Tₙ = a + (n − 1)d = 13 + (n − 1) × −3 = −3n + 16
7.Find the 22th term of the arithmetic sequence 7, 13, 19, 25, …
Answer: 133
- a = 7, d = 6
- T22 = 7 + 21 × 6 = 133
8.For the geometric sequence 7, 35, 175, 875, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 7 × 5n − 1
- r = 35 ÷ 7 = 5
9.For the geometric sequence 1, 5, 25, 125, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 1 × 5n − 1
- r = 5 ÷ 1 = 5
10.Find the sum of the first 11 terms of the arithmetic sequence 2, −1, −4, −7, …
Answer: −143
- Sₙ = n/2 × (2a + (n − 1)d)
- = 11/2 × (2 × 2 + 10 × −3)
- = −143
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