10th Grade Arithmetic and Geometric Sequences Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the 10th Grade sequences & series worksheet.
Success TutoringWorksheetsAnswer sheet10th Grade · Mathematics · Sequences & Series10th 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 −4, −20, −100, −500, …, write the common ratio and the rule for the nth term.
Answer: r = 5; Tₙ = −4 × 5n − 1
- r = −20 ÷ (−4) = 5
2.Find the sum of the first 6 terms of the geometric sequence −5, −25, −125, −625, …
Answer: −19530
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = −5 × (56 − 1) ÷ (5 − 1)
- = −19530
3.For the geometric sequence −2, −6, −18, −54, …, write the common ratio and the rule for the nth term.
Answer: r = 3; Tₙ = −2 × 3n − 1
- r = −6 ÷ (−2) = 3
4.For the geometric sequence 1, 4, 16, 64, …, write the common ratio and the rule for the nth term.
Answer: r = 4; Tₙ = 1 × 4n − 1
- r = 4 ÷ 1 = 4
5.Find the sum of the first 9 terms of the geometric sequence 3, 6, 12, 24, …
Answer: 1533
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 3 × (29 − 1) ÷ (2 − 1)
- = 1533
6.Find the 9th term of the arithmetic sequence 7, 4, 1, −2, …
Answer: −17
- a = 7, d = −3
- T9 = 7 + 8 × −3 = −17
7.Find the 6th term of the geometric sequence 7, −14, 28, −56, …
Answer: −224
- a = 7, r = −2
- T6 = 7 × (−2)5 = −224
8.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
9.For the arithmetic sequence 0, 9, 18, 27, …, write the common difference and the rule for the nth term.
Answer: d = 9; Tₙ = 9n − 9
- d = 9 − 0 = 9
- Tₙ = a + (n − 1)d = 0 + (n − 1) × 9 = 9n − 9
10.Find the sum of the first 5 terms of the geometric sequence 6, 18, 54, 162, …
Answer: 726
- Sₙ = a(rⁿ − 1) ÷ (r − 1)
- = 6 × (35 − 1) ÷ (3 − 1)
- = 726
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