Explanation Given information: a 1 = 2 , a n + 1 = 1 − 1 3 a n Calculation: The given recursive sequence is a 1 = 2 and a n + 1 = 1 − 1 3 a n For all n ∈ ℕ , let us calculate the values of the first eight terms of the sequence. a 1 = 2 a 2 = 1 3 a 1 = 1 − 1 3 ( 2 ) ≈ 0.3333 a 3 = 1 3 a 2 ≈ 1 − 1 3 0.3333 = 0.8889 a 4 = 1 3 a 3 ≈ 1 − 1 3 0.8889 ≈ 0.7037 a 5 = 1 3 a 4 ≈ 1 − 1 3 0.7037 ≈ 0.7654 a 6 = 1 3 a 5 = 1 − 1 3 0

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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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 2.1, Problem 28E

To determine

To calculate: the first eight terms of a1=2,an+1=1−13an to four decimal places and if it is convergent then fid its limit also.

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Chapter 2.1, Problem 27E

Chapter 2.1, Problem 29E

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Chapter 2 Solutions

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the first eight terms of a 1 = 2 , a n + 1 = 1 − 1 3 a n to four decimal places and if it is convergent then fid its limit also.

Solution Summary: The author calculates the values of the first eight terms of a_1=2, if it is convergent then fid its limit also.

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To calculate: the first eight terms of a1=2,an+1=1−13an to four decimal places and if it is convergent then fid its limit also.

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Chapter 2 Solutions