Explanation Given information: a 1 = 100 , a n + 1 = 1 2 ( a n + 25 a n ) Calculation: The given recursive sequence is a 1 = 100 and a n + 1 = 1 2 ( a n + 25 a n ) For all n , let us calculate the eight terms of the sequence up to four decimal places a 1 = 100 a 2 = 1 2 ( a 1 + 25 a 1 ) = a n + 1 = 1 2 ( 100 + 25 100 ) = 50.1250 a 3 = 1 2 ( a 2 + 25 a 2 ) = 1 2 ( 50.1250 + 25 50.1250 ) ≈ 25.3119 a 4 = 1 2 ( a 3 + 25 a 3 ) ≈ 1 2 ( 25.3119 + 25 25.3119 ) ≈ 13.1498 a 5 = 1 2 ( a 4 + 25 a 4 ) ≈ 1 2 ( 13.1498 + 25 13.1498 ) ≈ 7.525 a 6 = 1 2 ( a 5 + 25 a 5 ) ≈ 1 2 ( 7.525 + 25 7

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 2.1, Problem 34E

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To calculate: the first eight terms of a1=100,an+1=12(an+25an) to four decimal places and if it is convergent then fid its limit also.

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Chapter 2.1, Problem 33E

Chapter 2.1, Problem 35E

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Chapter 2 Solutions

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the first eight terms of a 1 = 100 , a n + 1 = 1 2 ( a n + 25 a n ) to four decimal places and if it is convergent then fid its limit also.

Solution Summary: The author calculates the eight terms of the sequence up to four decimal places and if it is convergent then fid its limit also.

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To calculate: the first eight terms of a1=100,an+1=12(an+25an) to four decimal places and if it is convergent then fid its limit also.

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Chapter 2 Solutions