Explanation Given information: The sequence a n = sin ( n π 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 = sin ( n π 3 ) . For the first term a 1 of the sequence put n = 1 , in formula a n = sin ( n π 3 ) , a 1 = sin ( 1 π 3 ) = sin ( π 3 ) = 3 2 Therefore, first term is 3 2 . For the second term a 2 of the sequence put n = 2 , in formula a n = sin ( n π 3 ) , a 2 = sin ( 2 π 3 ) = sin ( π − π 3 ) Recall the trigonometric formula, sin ( π − θ ) = sin θ and apply it, a 2 = sin ( π 3 ) = 3 2 Therefore, second term is 3 2 . For the third term a 3 of the sequence put n = 3 , in formula a n = sin ( n π 3 ) , a 3 = sin ( 3 π 3 ) = sin ( π ) = 0 Therefore, third term is 0

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 1, Problem 36E

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To calculate: The first six terms of the sequence an=sin(nπ3) .

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Chapter 1, Problem 35E

Chapter 1, Problem 37E

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Chapter 1 Solutions

Biocalculus

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The first six terms of the sequence a n = sin ( n π 3 ) .

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 sequence an=sin(nπ3) .

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Chapter 1 Solutions