Explanation Given: The sequence is a n + 1 = 1 2 a n +3 and a 0 = 1000 (1) Calculation: Obtain the ten terms of the sequence. Substitute 0 for n in equation (1), a 0 + 1 = 1 2 a 0 + 3 = 1 2 1000 + 3 [ ∵ a 0 = 1000 ] ≈ 15.811 + 3 = 18.811 Therefore the second term of the sequence is, a 1 ≈ 18.811 . Substitute 1 for n in equation (1), a 1 + 1 = 1 2 a 1 + 3 ≈ 1 2 18.811 + 3 [ ∵ a 1 ≈ 18.811 ] ≈ 2.1686 + 3 = 5.1686 Therefore, the third term of the sequence is, a 2 ≈ 5.1686 . Substitute 2 for n in equation (1), a 2 + 1 = 1 2 a 2 + 3 = 1 2 5.1686 + 3 [ ∵ a 2 ≈ 5.1686 ] ≈ 1.1367 + 3 = 4.1367 Therefore, the fourth term of the sequence is, a 3 = 4.1367 . Substitute 3 for n in equation (1), a 3 + 1 = 1 2 a 3 + 3 ≈ 1 2 4.1367 + 3 [ ∵ a 3 ≈ 4.1367 ] ≈ 1.0169 + 3 = 4.0169 Therefore, the fifth term of the sequence is, a 4 ≈ 4.0169 . Substitute 4 for n in equation (1). a 4 + 1 = 1 2 a 4 + 3 ≈ 1 2 4.0169 + 3 [ ∵ a 4 ≈ 4.0169 ] ≈ 1.0021 + 3 = 4.0021 Thus, the sixth term of the sequence is a 5 ≈ 4.0021 . Substitute 5 for n in equation (1), a 5 + 1 = 1 2 a 5 + 3 ≈ 1 2 4

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ISBN: 9781323178522

Author: Briggs

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 53E

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A plausible limit of the sequence if the sequence is convergent or state the sequence if diverges.

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Chapter 8.1, Problem 52E

Chapter 8.1, Problem 54E

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A plausible limit of the sequence if the sequence is convergent or state the sequence if diverges.

Solution Summary: The author explains how the sequence converges to 4. Substitute 0 for n in equation (1), c

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A plausible limit of the sequence if the sequence is convergent or state the sequence if diverges.

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Chapter 8 Solutions