12th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — 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 3 — Practice Set 4 — Answers
Arithmetic: Tₙ = a + (n − 1)d. Geometric: Tₙ = arn − 1. Show your work.
1.Find the 28th term of the arithmetic sequence −1, 4, 9, 14, …
Answer: 134
- a = −1, d = 5
- T28 = −1 + 27 × 5 = 134
2.Find the sum of the first 9 terms of the arithmetic sequence 15, 24, 33, 42, …
Answer: 459
- Sₙ = n/2 × (2a + (n − 1)d)
- = 9/2 × (2 × 15 + 8 × 9)
- = 459
3.For the geometric sequence 2, 10, 50, 250, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = 2 × 5n − 1
- r = 10 ÷ 2 = 5
4.Find the sum of the first 23 terms of the arithmetic sequence 2, 8, 14, 20, …
Answer: 1564
- Sₙ = n/2 × (2a + (n − 1)d)
- = 23/2 × (2 × 2 + 22 × 6)
- = 1564
5.Find the sum of the first 8 terms of the geometric sequence 2, 6, 18, 54, …
Answer: 6560
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 2 × (38 − 1) ÷ (3 − 1)
- = 6560
6.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
7.Find the sum of the first 9 terms of the geometric sequence 6, 12, 24, 48, …
Answer: 3066
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (29 − 1) ÷ (2 − 1)
- = 3066
8.Find the 16th term of the arithmetic sequence 19, 21, 23, 25, …
Answer: 49
- a = 19, d = 2
- T16 = 19 + 15 × 2 = 49
9.For the arithmetic sequence −6, 0, 6, 12, …, write the common difference and the rule for the nth term.
Answer: d = 6; Tₙ = 6n − 12
- d = 0 − (−6) = 6
- Tₙ = a + (n − 1)d = −6 + (n − 1) × 6 = 6n − 12
10.Find the 7th term of the geometric sequence 7, 21, 63, 189, …
Answer: 5103
- a = 7, r = 3
- T7 = 7 × 36 = 5103
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