Explanation The given recursive sequence is, x n + 1 = 1 2 ( x n + N x n ) , x 1 = N 2 and N = 10 . Substitute N = 10 in x 1 = N 2 . x 1 = 10 2 = 5 Obtain the six th terms of the sequence by substituting n = 1 , 2 , 3 , 4 and 5 in the expression x n + 1 = 1 2 ( x n + N x n ) as follows. x 1 + 1 = 1 2 ( x 1 + 10 x 1 ) x 2 = 1 2 ( 5 + 10 5 ) ( ∵ x 1 = 5 ) x 2 = 1 2 ( 5 + 2 ) x 2 = 7 2 That is, x 2 = 3.5 . Similarly, when n = 2 the sequence becomes, x 2 + 1 = 1 2 ( x 2 + 10 x 2 ) x 3 = 1 2 ( 3.5 + 10 3.5 ) ( ∵ x 2 = 3.5 ) x 3 ≈ 1 2 ( 3.5 + 2.86 ) x 3 ≈ 6.36 2 That is, x 3 ≈ 3.18 When n = 3 the sequence becomes, x 3 + 1 = 1 2 ( x 3 + 10 x 3 ) x 4 = 1 2 ( 3

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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 30.1, Problem 48E

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The six^th term x6 of the given recursive sequence and compare it with 10 and conclude that N can be approximated by this recursion sequence.

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Chapter 30.1, Problem 47E

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Chapter 30 Solutions

Basic Technical Mathematics

Ch. 30.1 - Prob. 1PE Ch. 30.1 - Prob. 2PE Ch. 30.1 - Prob. 1E Ch. 30.1 - Prob. 2E Ch. 30.1 - Prob. 3E Ch. 30.1 - Prob. 4E Ch. 30.1 - Prob. 5E Ch. 30.1 - Prob. 6E Ch. 30.1 - Prob. 7E Ch. 30.1 - Prob. 8E

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The six th term x 6 of the given recursive sequence and compare it with 10 and conclude that N can be approximated by this recursion sequence.

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The sixth term x6 of the given recursive sequence and compare it with 10 and conclude that N can be approximated by this recursion sequence.

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The six^th term x6 of the given recursive sequence and compare it with 10 and conclude that N can be approximated by this recursion sequence.