Explanation Given information: The recursive sequence a n + 1 = a n 1 + a n and first term, a 1 = 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 + 1 = a n 1 + a n whose first term, a 1 = 2 . 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 = a n 1 + a n , a 1 + 1 = a 1 1 + a 1 a 2 = a 1 1 + a 1 Substitute the value of a 1 which is 2, to generate the second term, a 2 = 2 1 + 2 a 2 = 2 3 Therefore, the second term is 2 3 . 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 = a n 1 + a n , a 2 + 1 = a 2 1 + a 2 a 3 = a 2 1 + a 2 Substitute the value of a 2 which is 2 3 , to generate the third term, a 3 = 2 3 1 + 2 3 a 3 = 2 3 5 3 a 3 = 2 5 Therefore, the third term is 2 5 . 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 = a n 1 + a n , a 3 + 1 = a 3 1 + a 3 a 4 = a 3 1 + a 3 Substitute the value of a 3 which is 3, to generate the fourth term, a 4 = 2 5 1 + 2 5 a 4 = 2 5 7 5 a 4 = 2 7 Therefore, the fourth term is 2 7

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ISBN: 9781305177291

Author: James Stewart, Troy Day

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 17E

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To calculate: The first six terms of the recursive sequence an+1=an1+an whose first term is 2.

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Chapter 1.6, Problem 16E

Chapter 1.6, Problem 18E

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Chapter 1 Solutions

Biocalculus: Calculus For Life Sciences

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

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

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To calculate: The first six terms of the recursive sequence an+1=an1+an whose first term is 2.

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Chapter 1 Solutions