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List the first five terms of the sequence. a1 = 2, : 2, a n + 1 an + 1 = 2an + 4 21 2 а2 8 12 14 16 аз ад a5 = = ххх x

List the first five terms of the sequence. a1 = 2, : 2, a n + 1 an + 1 = 2an + 4 21 2 а2 8 12 14 16 аз ад a5 = = ххх x

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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**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.
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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