Answered: Use inductive reasoning to predict the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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reasoning is the process of reaching a general conclusion by examining specific examples. EXAMPLE 1. Use Inductive Reasoning to Predict a Number Use inductive reasoning to predict the next number in each of the following lists. a. 3, 6, 8, 12, 15, ? b.) 1, 3, ,6, 10, 15, ? Solution. a.) Each successive number is 3 larger than the preceding number. Thus we predict that the next number in the list is 3 larger than 15, which is 18. b.) The first two numbers differ by 2. The second and third number differs by 3. It appears that the difference between any two numbers is always 1 more than the preceding difference. Since 10 and 15 differ by 5, we predict that the next number in the list will be 6 larger than 15 which is 21
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		1921
		2401
		7776
		16807
		1967

Use inductive reasoning to predict the most probable next number in the given list. ​ 81, 256, 625, 1296, ? ​ 1921 2401 7776 16807 1967

Use inductive reasoning to predict the most probable next number in the given list. 81, 256, 625, 1296, ? 1921 2401 7776 16807 1967