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

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 1.6, Problem 22E

To determine

To calculate: The first six terms of the recursive sequence an+2=an+1+2an whose first term is 1 and second term is 2.

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Chapter 1.6, Problem 21E

Chapter 1.6, Problem 23E

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Chapter 1 Solutions

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

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The first six terms of the recursive sequence a n + 2 = a n + 1 + 2 a n whose first term is 1 and second term is 2.

Solution Summary: The author calculates the first six terms of the recursive sequence a_n+2 and the third term by substituting the previous terms.

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To calculate: The first six terms of the recursive sequence an+2=an+1+2an whose first term is 1 and second term is 2.

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Chapter 1 Solutions