Explanation Given information: The recursive sequence a n + 1 = 3 a n 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 = 3 a n 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 = 3 a n , a 1 + 1 = 3 a 1 a 2 = 3 a 1 Substitute the value of a 1 which is 1, to generate the second term, a 2 = 3 a 1 a 2 = 3 ( 1 ) a 2 = 3 1 2 Therefore, the second term is 3 1 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 = 3 a n , a 2 + 1 = 3 a 2 a 3 = 3 a 2 Substitute the value of a 2 which is 3 1 2 , to generate the third term, a 3 = 3 ( 3 1 2 ) a 3 = 3 3 2 a 3 = 3 3 4 Therefore, the third term is 3 3 4 . For the fourth term a 4 of the sequence, substitute the previous term, that is put n = 3 , in the recursive formula a n + 1 = 3 a n , a 3 + 1 = 3 a 3 a 4 = 3 a 3 Substitute the value of a 3 which is 3 3 4 , to generate the fourth term, a 4 = 3 ( 3 3 4 ) a 4 = 3 7 4 a 4 = 3 7 8 Therefore, the fourth term is 3 7 8

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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Chapter 1.6, Problem 19E

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

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Chapter 1.6, Problem 18E

Chapter 1.6, Problem 20E

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Chapter 1 Solutions

Biocalculus

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The first six terms of the recursive sequence a n + 1 = 3 a n whose first term is 1.

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

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Chapter 1 Solutions