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:**List the First Five Terms of the Sequence**
Given:
\( a_1 = 2 \)
\( a_{n+1} = 2a_n + 4 \)
Calculate the first five terms of the sequence:
- \( a_1 = 2 \) ✔️
- \( a_2 = 8 \) ✔️
- \( a_3 = 12 \) ✖️
- \( a_4 = 14 \) ✖️
- \( a_5 = 16 \) ✖️
**Explanation:**
The sequence starts with the initial term \( a_1 = 2 \). According to the formula \( a_{n+1} = 2a_n + 4 \), the next term is obtained by doubling the previous term and adding 4.
1. \( a_1 = 2 \)
2. \( a_2 = 2(2) + 4 = 8 \)
3. \( a_3 = 2(8) + 4 = 20 \) (the correct next term after a mistake)
4. \( a_4 = 2(20) + 4 = 44 \)
5. \( a_5 = 2(44) + 4 = 92 \)
The provided answers for \( a_3 \), \( a_4 \), and \( a_5 \) in the image are incorrect based on the given formula.
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