Explanation Given information: The first few terms of the sequence are − 3 , 2 , − 4 3 , 8 9 , − 16 27 , … . 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 − 3 , 2 , − 4 3 , 8 9 , − 16 27 , … . First term of the sequence is a 1 = − 3 . Second term of the sequence is a 2 = 2 . Third term of the sequence is a 3 = − 4 3 . Fourth term of the sequence is a 4 = 8 9 . Fifth term of the sequence is a 5 = − 16 27 . Observe that first term is − 3 , the second term is obtained is multiplying the first term by ( − 2 3 ) . Similarly the third obtained is multiplying the second term by ( − 2 3 ) and so on. Now the first term can be written as, a 1 = − 3 = ( − 3 ) ( − 2 3 ) 1 − 1 = ( − 3 ) 0 Similarly the second term can be written as, a 2 = 2 = ( − 3 ) ( − 2 3 ) 2 − 1 Similarly the third term can be written as, a 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 11E

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To calculate: The general term an of the sequence whose first few terms are −3,2,−43,89,−1627,… .

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Chapter 1.6, Problem 10E

Chapter 1.6, Problem 12E

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Chapter 1 Solutions

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 − 3 , 2 , − 4 3 , 8 9 , − 16 27 , … .

Solution Summary: The author calculates the general term a_n of the sequence whose first few terms are -3,2,-43

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To calculate: The general term an of the sequence whose first few terms are −3,2,−43,89,−1627,… .

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Chapter 1 Solutions