Explanation Given information: The recursive sequence a n + 1 = 5 a n − 3 and first term, a 1 = 1 . Formula used: For a recursive sequence of the form a n + 1 , whose first term is known the next terms of the sequence are generated by substituting the previous term to the recursive formula. Calculation: Consider the recursive sequence a n + 1 = 5 a n − 3 whose first term, a 1 = 1 . For the second term a 2 of the sequence, substitute the previous term, that is put n = 1 , in the recursive formula a n + 1 = 5 a n − 3 , a 1 + 1 = 5 a 1 − 3 a 2 = 5 a 1 − 3 Substitute the value of a 1 which is 1, to generate the second term, a 2 = 5 a 1 − 3 a 2 = 5 ( 1 ) − 3 a 2 = 5 − 3 a 2 = 2 Therefore, the second term is 2. For the third term a 3 of the sequence, substitute the previous term, that is put n = 2 , in the recursive formula a n + 1 = 5 a n − 3 , a 2 + 1 = 5 a 2 − 3 a 3 = 5 a 2 − 3 Substitute the value of a 2 which is 2, to generate the third term, a 3 = 5 a 2 − 3 a 3 = 5 ( 2 ) − 3 a 3 = 10 − 3 a 3 = 7 Therefore, the third term is 7

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

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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Question

Chapter 1.6, Problem 15E

To determine

To calculate:The first six terms of the recursive sequence an+1=5an−3 whose first term is 1.

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Chapter 1.6, Problem 14E

Chapter 1.6, Problem 16E

Chapter 1 Solutions

Biocalculus

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - Prob. 51E Ch. 1.1 - Prob. 52E Ch. 1.1 - Prob. 53E Ch. 1.1 - Prob. 54E Ch. 1.1 - Prob. 55E Ch. 1.1 - Prob. 56E Ch. 1.1 - Prob. 57E Ch. 1.1 - Prob. 58E Ch. 1.1 - Prob. 59E Ch. 1.1 - Prob. 60E Ch. 1.1 - 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The first six terms of the recursive sequence a n + 1 = 5 a n − 3 whose first term is 1.

Solution Summary: The author calculates the first six terms of the recursive sequence a_n+1=5

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To calculate:The first six terms of the recursive sequence an+1=5an−3 whose first term is 1.

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Chapter 1 Solutions