12th Grade Arithmetic and Geometric Sequences Worksheet — Level 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 2 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 14th term of the arithmetic sequence 17, 23, 29, 35, …
Answer: 95
- a = 17, d = 6
- T14 = 17 + 13 × 6 = 95
2.Find the sum of the first 7 terms of the geometric sequence 2, 10, 50, 250, …
Answer: 39062
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (57 − 1) ÷ (5 − 1)
- = 39062
3.Find the sum of the first 7 terms of the geometric sequence 1, 2, 4, 8, …
Answer: 127
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 1 × (27 − 1) ÷ (2 − 1)
- = 127
4.For the arithmetic sequence −2, 6, 14, 22, …, write the common difference and the rule for the nth term.
Answer: d = 8; Tₙ = 8n − 10
- d = 6 − (−2) = 8
- Tₙ = a + (n − 1)d = −2 + (n − 1) × 8 = 8n − 10
5.Find the sum of the first 15 terms of the arithmetic sequence 12, 21, 30, 39, …
Answer: 1125
- Sₙ = n/2 × (2a + (n − 1)d)
- = 15/2 × (2 × 12 + 14 × 9)
- = 1125
6.For the geometric sequence −4, −8, −16, −32, …, write the common ratio and the rule for the nth term.
Answer: r = 2; Tₙ = −4 × 2n − 1
- r = −8 ÷ (−4) = 2
7.Find the 6th term of the geometric sequence 5, 10, 20, 40, …
Answer: 160
- a = 5, r = 2
- T6 = 5 × 25 = 160
8.For the geometric sequence −3, −12, −48, −192, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = −3 × 4n − 1
- r = −12 ÷ (−3) = 4
9.Find the 26th term of the arithmetic sequence −3, 6, 15, 24, …
Answer: 222
- a = −3, d = 9
- T26 = −3 + 25 × 9 = 222
10.Find the sum of the first 7 terms of the geometric sequence 4, −8, 16, −32, …
Answer: 172
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 4 × ((−2)7 − 1) ÷ (−2 − 1)
- = 172
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