Explanation Given information: The sequence a n + 1 = n + 2 a n − 1 and first term, a 1 = 3 . 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 = n + 2 a n − 1 whose first term, a 1 = 3 . For the second term a 2 of the sequence, substitute the previous terms, that is put n = 1 , in the recursive formula a n + 1 = n + 2 a n − 1 , a 1 + 1 = n + 2 a 1 − 1 a 2 = 1 + 2 a 1 − 1 a 2 = 2 a 1 Substitute the value of a 1 which is 2, to generate the second term, a 2 = 2 ( 3 ) a 2 = 6 Therefore, the second term is 6. For the third term a 3 of the sequence, substitute the previous terms, that is put n = 2 , in the recursive formula a n + 1 = n + 2 a n − 1 , a 2 + 1 = n + 2 a 2 − 1 a 3 = 2 + 2 a 2 − 1 a 3 = 1 + 2 a 2 Substitute the value of a 1 which is 2, to generate the second term, a 3 = 1 + 2 ( 6 ) a 3 = 13 Therefore, the second term is 13

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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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, Problem 37E

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To calculate: The first six terms of the sequence an+1=n+2an−1 whose first term is 3.

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Chapter 1, Problem 36E

Chapter 1, Problem 38E

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Chapter 1 Solutions

BIOCALCULUS:CALCULUS F/LIFE...-W/ACCESS

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The first six terms of the sequence a n + 1 = n + 2 a n − 1 whose first term is 3.

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To calculate: The first six terms of the sequence an+1=n+2an−1 whose first term is 3.

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Chapter 1 Solutions