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
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...
icon
Related questions
Question
**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.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 6 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning