12th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 7th term of the geometric sequence 3, −6, 12, −24, …
Answer: 192
- a = 3, r = −2
- T7 = 3 × (−2)6 = 192
2.Find the sum of the first 9 terms of the geometric sequence −1, −4, −16, −64, …
Answer: −87381
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −1 × (49 − 1) ÷ (4 − 1)
- = −87381
3.Find the 20th term of the arithmetic sequence −5, −8, −11, −14, …
Answer: −62
- a = −5, d = −3
- T20 = −5 + 19 × −3 = −62
4.For the geometric sequence −3, −9, −27, −81, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −3 × 3n − 1
- r = −9 ÷ (−3) = 3
5.Find the sum of the first 8 terms of the arithmetic sequence −1, 2, 5, 8, …
Answer: 76
- Sₙ = n/2 × (2a + (n − 1)d)
- = 8/2 × (2 × −1 + 7 × 3)
- = 76
6.Find the 13th term of the arithmetic sequence 12, 13, 14, 15, …
Answer: 24
- a = 12, d = 1
- T13 = 12 + 12 × 1 = 24
7.Find the sum of the first 6 terms of the geometric sequence −3, 6, −12, 24, …
Answer: 63
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × ((−2)6 − 1) ÷ (−2 − 1)
- = 63
8.Find the sum of the first 15 terms of the arithmetic sequence 17, 15, 13, 11, …
Answer: 45
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × 17 + 14 × −2)
- = 45
9.Find the 9th term of the geometric sequence −1, 2, −4, 8, …
Answer: −256
- a = −1, r = −2
- T9 = −1 × (−2)8 = −256
10.Find the sum of the first 8 terms of the geometric sequence 5, 20, 80, 320, …
Answer: 109225
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 5 × (48 − 1) ÷ (4 − 1)
- = 109225
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