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
![**Instructions:**
List the first five terms of the sequence.
**Given:**
\[ a_1 = 5 \]
\[ a_{n+1} = 2a_n + 4 \]
**Tasks:**
- Find the values of \( a_1, a_2, a_3, a_4, a_5 \).
**Solution Steps:**
1. **Calculate \( a_2 \):**
\[ a_2 = 2a_1 + 4 = 2 \times 5 + 4 = 14 \]
2. **Calculate \( a_3 \):**
\[ a_3 = 2a_2 + 4 = 2 \times 14 + 4 = 32 \]
3. **Calculate \( a_4 \):**
\[ a_4 = 2a_3 + 4 = 2 \times 32 + 4 = 68 \]
4. **Calculate \( a_5 \):**
\[ a_5 = 2a_4 + 4 = 2 \times 68 + 4 = 140 \]
**Results:**
- \( a_1 = 5 \)
- \( a_2 = 14 \)
- \( a_3 = 32 \)
- \( a_4 = 68 \)
- \( a_5 = 140 \)
**Summary:**
The first five terms of the sequence are: 5, 14, 32, 68, and 140.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39b0ab21-1d86-470a-a1a2-88c4e7c0de49%2Fb27b13b5-38ee-46d3-bbfe-71169e922271%2F68go2cw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instructions:**
List the first five terms of the sequence.
**Given:**
\[ a_1 = 5 \]
\[ a_{n+1} = 2a_n + 4 \]
**Tasks:**
- Find the values of \( a_1, a_2, a_3, a_4, a_5 \).
**Solution Steps:**
1. **Calculate \( a_2 \):**
\[ a_2 = 2a_1 + 4 = 2 \times 5 + 4 = 14 \]
2. **Calculate \( a_3 \):**
\[ a_3 = 2a_2 + 4 = 2 \times 14 + 4 = 32 \]
3. **Calculate \( a_4 \):**
\[ a_4 = 2a_3 + 4 = 2 \times 32 + 4 = 68 \]
4. **Calculate \( a_5 \):**
\[ a_5 = 2a_4 + 4 = 2 \times 68 + 4 = 140 \]
**Results:**
- \( a_1 = 5 \)
- \( a_2 = 14 \)
- \( a_3 = 32 \)
- \( a_4 = 68 \)
- \( a_5 = 140 \)
**Summary:**
The first five terms of the sequence are: 5, 14, 32, 68, and 140.
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