Explanation Given: Density of female insects during the first year is 500 per acre with r = 0.8 . Calculation: (a) Let a n denotes the density of female insects during the n t h year. Since density of female insects during the first year is 500, thus, a 1 = 500 Also r = 0.8 , therefore, a n = r × a n − 1 = 0.8 a n − 1 Thus, recursive sequence is defined as a 1 = 500 , a n = 0.8 a n − 1 (b) Part (a) can be used to find the first six terms of the sequence. From part (a) a 1 = 500 Therefore, a 2 = 0.8 a 2 − 1 = 0.8 a 1 = 0.8 × 500 = 400 a 3 = 0.8 a 3 − 1 = 0.8 a 2 = 0.8 × 400 = 320 a 4 = 0.8 a 4 − 1 = 0.8 a 3 = 0.8 × 320 = 256 a 5 = 0.8 a 5 − 1 = 0.8 a 4 = 0.8 × 256 = 204.8 a 6 = 0.8 a 6 − 1 = 0.8 a 5 = 0.8 × 204.8 = 163.84 First six terms are a 1 = 500 , a 2 = 400 , a 3 = 320 , a 4 = 256 , a 5 = 204...

College Algebra with Modeling & Visualization (5th Edition)

5th Edition

ISBN: 9780321826138

Author: Gary K. Rockswold

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 89E

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The recursive sequence that describes the given data. Find first six terms of the sequence and to find the general term $a_{n}$ .

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Chapter 8.1, Problem 88E

Chapter 8.1, Problem 90E

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Chapter 8 Solutions

College Algebra with Modeling & Visualization (5th Edition)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The recursive sequence that describes the given data. Find first six terms of the sequence and to find the general term a n .

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The recursive sequence that describes the given data. Find first six terms of the sequence and to find the general term an .

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Chapter 8 Solutions

The recursive sequence that describes the given data. Find first six terms of the sequence and to find the general term $a_{n}$ .