a. Explanation Given: The pattern of compensation is described by x n + 1 = 1 2 ( x n + x n − 1 ) for n = 1 , 2 , 3 , ⋯ (1) The number of hours of sleep on the first two nights are x 0 = 7 and x 1 = 6 . Calculation: From the given, the first two terms of the sequence are x 0 = 7 and x 1 = 6 . Substitute 1 for x in equation (1), x 1 + 1 = 1 2 ( x 1 + x 1 − 1 ) x 2 = 1 2 ( 6 + 7 ) ( ∵ x 0 = 7 and x 1 = 6 ) = 1 2 ( 13 ) = 6.5 Thus, the third term of the sequence is x 2 = 6.5 . Substitute 2 for x in equation (1), x 2 + 1 = 1 2 ( x 2 + x 1 ) x 3 = 1 2 ( 6.5 + 6 ) ( ∵ x 1 = 6 and x 2 = 6.5 ) = 1 2 ( 12.5 ) = 6.25 Thus, the fourth term of the sequence is x 3 = 6.25 . Substitute 3 for x in equation (1), x 3 + 1 = 1 2 ( x 3 + x 2 ) x 4 = 1 2 ( 6 b. To determine To show: The explicit formula x n = 19 3 + 2 3 ( − 1 2 ) n , for n ≥ 0 . c. To determine To find: The limit of the sequence.

Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)

2nd Edition

ISBN: 9780321965172

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 8.2, Problem 94E

To determine

To write: The first six terms of the sequence {xn} and confirm that the terms alternately increase and decrease.

To determine

To show: The explicit formula xn=193+23(−12)n, for n≥0.

To determine

To find: The limit of the sequence.

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Chapter 8.2, Problem 93E

Chapter 8.2, Problem 95E

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Chapter 8 Solutions

Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)

Ch. 8.1 - Prob. 1QC Ch. 8.1 - Prob. 2QC Ch. 8.1 - Prob. 3QC Ch. 8.1 - Prob. 4QC Ch. 8.1 - Prob. 5QC Ch. 8.1 - Define sequence and give an example.Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Suppose the sequence {an} is defined by the...Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E

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The first six terms of the sequence { x n } and confirm that the terms alternately increase and decrease.

Solution Summary: The author explains how the first six terms of the sequence are leftx_nright and confirm that the terms alternately increase and decrease.

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To write: The first six terms of the sequence {xn} and confirm that the terms alternately increase and decrease.

To show: The explicit formula xn=193+23(−12)n, for n≥0.

To find: The limit of the sequence.

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