12th Grade Arithmetic and Geometric Sequences Worksheet — Level 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 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.For the geometric sequence 1, 2, 4, 8, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = 1 × 2n − 1
- r = 2 ÷ 1 = 2
2.Find the sum of the first 8 terms of the geometric sequence 8, 40, 200, 1000, …
Answer: 781248
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 8 × (58 − 1) ÷ (5 − 1)
- = 781248
3.Find the sum of the first 5 terms of the geometric sequence 6, −12, 24, −48, …
Answer: 66
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × ((−2)5 − 1) ÷ (−2 − 1)
- = 66
4.For the arithmetic sequence 15, 24, 33, 42, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n + 6
- d = 24 − 15 = 9
- Tₙ = a + (n − 1)d = 15 + (n − 1) × 9 = 9n + 6
5.Find the sum of the first 7 terms of the geometric sequence −3, −15, −75, −375, …
Answer: −58593
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −3 × (57 − 1) ÷ (5 − 1)
- = −58593
6.Find the sum of the first 9 terms of the geometric sequence 6, 24, 96, 384, …
Answer: 524286
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (49 − 1) ÷ (4 − 1)
- = 524286
7.Find the 7th term of the geometric sequence −5, 10, −20, 40, …
Answer: −320
- a = −5, r = −2
- T7 = −5 × (−2)6 = −320
8.Find the 8th term of the geometric sequence 7, −14, 28, −56, …
Answer: −896
- a = 7, r = −2
- T8 = 7 × (−2)7 = −896
9.Find the sum of the first 5 terms of the geometric sequence −5, −20, −80, −320, …
Answer: −1705
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (45 − 1) ÷ (4 − 1)
- = −1705
10.Find the 9th term of the geometric sequence 2, 4, 8, 16, …
Answer: 512
- a = 2, r = 2
- T9 = 2 × 28 = 512
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