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Which of the following sequences represents an arithmetic sequence with a common difference d = -5? 4, -20, 100, -500, 2,500 1,250, 250, 50, 10, 2 30, 25, 20, 15, 3 47, 42, 37, 32,27

Which of the following sequences represents an arithmetic sequence with a common difference d = -5? 4, -20, 100, -500, 2,500 1,250, 250, 50, 10, 2 30, 25, 20, 15, 3 47, 42, 37, 32,27

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question:** Which of the following sequences represents an arithmetic sequence with a common difference \( d = -5 \)? - 4, -20, 100, -500, 2,500 - 1,250, 250, 50, 10, 2 - 30, 25, 20, 15, 3 - 47, 42, 37, 32, 27 **Explanation:** An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference, \( d \). For this question, the common difference is given as \( d = -5 \). Let's analyze each sequence: 1. **4, -20, 100, -500, 2,500** Differences: -24, 120, -600, 3,000 (not constant) 2. **1,250, 250, 50, 10, 2** Differences: -1,000, -200, -40, -8 (not constant) 3. **30, 25, 20, 15, 3** Differences: -5, -5, -5, -12 (not consistent) 4. **47, 42, 37, 32, 27** Differences: -5, -5, -5, -5 (constant, each difference is -5) The correct sequence with a common difference of \( d = -5 \) is **47, 42, 37, 32, 27**.
Transcribed Image Text:**Question:** Which of the following sequences represents an arithmetic sequence with a common difference \( d = -5 \)? - 4, -20, 100, -500, 2,500 - 1,250, 250, 50, 10, 2 - 30, 25, 20, 15, 3 - 47, 42, 37, 32, 27 **Explanation:** An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference, \( d \). For this question, the common difference is given as \( d = -5 \). Let's analyze each sequence: 1. **4, -20, 100, -500, 2,500** Differences: -24, 120, -600, 3,000 (not constant) 2. **1,250, 250, 50, 10, 2** Differences: -1,000, -200, -40, -8 (not constant) 3. **30, 25, 20, 15, 3** Differences: -5, -5, -5, -12 (not consistent) 4. **47, 42, 37, 32, 27** Differences: -5, -5, -5, -5 (constant, each difference is -5) The correct sequence with a common difference of \( d = -5 \) is **47, 42, 37, 32, 27**.
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