Explanation Given: The sequence is a n + 1 = 2 a n +1 and a 0 = 0 (1) Calculation: Obtain the ten terms of the sequence. Substitute 0 for n in equation (1), a 0 + 1 = 2 a 0 + 1 = 2 ( 0 ) +1 [ ∵ a 0 = 0 ] = 0 + 1 = 1 Therefore the second term of the sequence is a 1 = 1 . Substitute 1 for n in equation (1), a 1 + 1 = 2 a 1 + 1 = 2 ( 1 ) +1 [ ∵ a 1 = 1 ] = 2 + 1 = 3 Therefore, the third term of the sequence is, a 2 = 3 . Substitute 2 for n in equation (1), a 2 + 1 = 2 a 2 + 1 = 2 ( 3 ) +1 [ ∵ a 2 = 3 ] = 6 + 1 = 7 Therefore, the fourth term of the sequence is, a 3 = 7 . Substitute 3 for n in equation (1), a 3 + 1 = 2 a 3 + 1 = 2 ( 7 ) +1 [ ∵ a 3 = 7 ] = 14 + 1 = 15 Therefore, the fifth term of the sequence is, a 4 = 15 . Substitute 4 for n in equation (1), a 4 + 1 = 2 a 4 + 1 = 2 ( 15 ) +1 [ ∵ a 4 = 15 ] = 30 + 1 = 31 Thus, the sixth term of the sequence is a 5 = 31 . Substitute 5 for n in equation (1), a 5 + 1 = 2 a 5 + 1 = 2 ( 31 ) +1 [ ∵ a 5 = 31 ] = 62 + 1 = 63 Thus, the seventh term of the sequence is a 6 = 63

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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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 8.1, Problem 51E

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A plausible limit of the sequence if the sequence converges or state the sequence if diverges.

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Chapter 8.1, Problem 50E

Chapter 8.1, Problem 52E

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Chapter 8 Solutions

Calculus: Early Transcendentals (2nd Edition)

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 Ch. 8.1 - Given the series k=1k, evaluate the first four...Ch. 8.1 - The terms of a sequence of partial sums are...Ch. 8.1 - Consider the infinite series k=11k. Evaluate the...Ch. 8.1 - Explicit formulas Write the first four terms of...Ch. 8.1 - Explicit formulas Write the first four terms of...

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A plausible limit of the sequence if the sequence converges or state the sequence if diverges.

Solution Summary: The author explains the sequence converges or diverges. Substitute 0 for n in equation (1), c

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A plausible limit of the sequence if the sequence converges or state the sequence if diverges.

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Chapter 8 Solutions