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
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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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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