Explanation The given sequence is a n = 1 2 ( a n − 1 + A a n − 1 ) and a 1 = A 2 . Compute the value of a 1 that takes the value of A as 6. a 1 = 6 2 = 3 Find each term of the sequence that starts with the index n = 2 to n = 4 as a 1 = 1 . Compute the term for n = 2 as follows. a 2 = 1 2 ( a 2 − 1 + 6 a 2 − 1 ) = 1 2 ( a 1 + 6 a 1 ) = 1 2 ( 3 + 6 3 ) = 1 2 ( 3 + 2 ) On further simplification the value of a 2 becomes, a 2 = 1 2 ( 3 + 2 ) = 1 2 × 5 = 2.5 Compute the term for n = 3 as follows. a 3 = 1 2 ( a 3 − 1 + 6 a 3 − 1 ) = 1 2 ( a 2 + 6 a 2 ) = 1 2 ( 2.5 + 6 2

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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 B.1, Problem 68E

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To find: The first four terms of the sequence an=12(an−1+Aan−1) for n≥2 when A=6 and to compare the fourth term with the value of A which is obtained from a calculator.

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Chapter B.1, Problem 67E

Chapter B.1, Problem 69E

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Chapter B.1 Solutions

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The first four terms of the sequence a n = 1 2 ( a n − 1 + A a n − 1 ) for n ≥ 2 when A = 6 and to compare the fourth term with the value of A which is obtained from a calculator.

Solution Summary: The author explains how to find the first four terms of the sequence a_n=12left when A=6 and to compare the fourth term with the value of

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To find: The first four terms of the sequence an=12(an−1+Aan−1) for n≥2 when A=6 and to compare the fourth term with the value of A which is obtained from a calculator.

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Chapter B.1 Solutions