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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, ?

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, ?

Advanced Engineering Mathematics
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
Transcribed Image Text: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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