Explanation Given information: The first few terms of the sequence are 1 , 0 , − 1 , 0 , 1 , 0 , − 1 , 0 , … . Formula used: Observe the pattern of numbers in the sequence to generate the general term of the sequence. Calculation: Consider, the first few terms of the sequence that are 1 , 0 , − 1 , 0 , 1 , 0 , − 1 , 0 , … . First term of the sequence is a 1 = 1 . Second term of the sequence is a 2 = 0 . Third term of the sequence is a 3 = − 1 . Fourth term of the sequence is a 4 = 0 . Fifth term of the sequence is a 5 = 1 . And so on. Observe that the values are oscillating between 1 and − 1 with zeros in between. Recall that range of some trigonometric functions lie between 1 and − 1 . Since, the value of cosine function at 0 is 1, at π 2 is 0, for odd multiple of π value is − 1 and for even multiple of π value is 1 . Therefore, general term can be formulated in terms of cosine function, cos ( π ( n − 1 ) 2 ) . Now the first term can be written as, a 1 = 1 = cos ( π ( 1 − 1 ) 2 ) = cos ( 0 ) Similarly the second term can be written as, a 2 = 0 = cos ( π ( 2 − 1 )

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 14E

To determine

To calculate: The general term an of the sequence whose first few terms are 1,0,−1,0,1,0,−1,0,… .

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Chapter 1.6, Problem 13E

Chapter 1.6, Problem 15E

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Chapter 1 Solutions

Biocalculus

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The general term a n of the sequence whose first few terms are 1 , 0 , − 1 , 0 , 1 , 0 , − 1 , 0 , … .

Solution Summary: The author calculates the general term a_n of the sequence whose first few terms are 1,0,-1,0. The first term can be formulated in terms of cosine function

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To calculate: The general term an of the sequence whose first few terms are 1,0,−1,0,1,0,−1,0,… .

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Chapter 1 Solutions