Explanation Given: The sequence is given as, a n = 2 ⋅ 3 n − 2 When, a n + 1 = 3 a n + 4 , a 1 = 4 Approach: Prove basic step for n = 1 . Assume the statement is true for some natural number n ≥ 1 and show that the statement is true for n + 1 . Calculation: Denote the statement “ a n = 2 ⋅ 3 n − 2 for all natural numbers n for the sequence defined recursively as a n + 1 = 3 a n + 4 , a 1 = 4 ” by P ( n ) . Step 1 : For, n = 1 a 1 = 4 = 2 ⋅ 3 1 − 2 This proves Step 1 . Step 2 : Assume P ( n ) is true for some n ≥ 1 . This is called the induction hypothesis

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Chapter 13.CR, Problem 72E

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To prove:

The statement an=2⋅3n−2 for all natural numbers n for the sequence defined recursively as an+1=3an+4,a1=4.

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Chapter 13.CR, Problem 71E

Chapter 13.CR, Problem 73E

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Chapter 13 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 13.1 - CONCEPTS A sequence is a function whose domain is...Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - 3-14, Terms of a Sequence Find the first four...Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

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To prove: The statement a n = 2 ⋅ 3 n − 2 for all natural numbers n for the sequence defined recursively as a n + 1 = 3 a n + 4 , a 1 = 4 .

Solution Summary: The author explains how to prove the statement a_n=2cdot, which is true for all natural numbers for the sequence defined recursively.

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To prove:

The statement an=2⋅3n−2 for all natural numbers n for the sequence defined recursively as an+1=3an+4,a1=4.

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Chapter 13 Solutions

To prove: The statement a n = 2 ⋅ 3 n − 2 for all natural numbers n for the sequence defined recursively as a n + 1 = 3 a n + 4 , a 1 = 4 .

Solution Summary: The author explains how to prove the statement a_n=2cdot, which is true for all natural numbers for the sequence defined recursively.

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Videos

To prove: The statement an=2⋅3n−2 for all natural numbers n for the sequence defined recursively as an+1=3an+4,a1=4.

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Chapter 13 Solutions

To prove:

The statement an=2⋅3n−2 for all natural numbers n for the sequence defined recursively as an+1=3an+4,a1=4.