Explanation Given information: The first few terms of the sequence are 1 , − 1 3 , 1 9 , − 1 27 , 1 81 , … . 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 , − 1 3 , 1 9 , − 1 27 , 1 81 , … . First term of the sequence is a 1 = 1 . Second term of the sequence is a 2 = − 1 3 . Third term of the sequence is a 3 = 1 9 . Fourth term of the sequence is a 4 = − 1 27 . Fifth term of the sequence is a 5 = 1 81 . Observe that numerator term of all the terms is same and the denominator is 3 n for n ≥ 0 . Since alternate signs are there with first term as positive so multiply the general term by ( − 1 ) n . Now the first term can be written as, a 1 = 1 = ( − 1 ) 0 1 3 0 Similarly the second term can be written as, a 2 = − 1 3 </

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 10E

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To calculate: The general term an of the sequence whose first few terms are 1,−13,19,−127,181,… .

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Chapter 1.6, Problem 9E

Chapter 1.6, Problem 11E

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Biocalculus

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E

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The general term a n of the sequence whose first few terms are 1 , − 1 3 , 1 9 , − 1 27 , 1 81 , … .

Solution Summary: The author calculates the general term a_n of the sequence whose first few terms are 1,-13,

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To calculate: The general term an of the sequence whose first few terms are 1,−13,19,−127,181,… .

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Chapter 1 Solutions