Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 1 - Problem Solving and Critical Thinking - 1.1 Inductive and Deductive Reasoning - Exercise Set 1.1: 54

Answer

987,654 yes

Work Step by Step

$\underline{Inductive\ Reasoning}$ Each result in the sequence is a number that is one digit longer than the prior result. The leading digits of the new result are the same digits as the prior result. The ones position is the one less than the digit in the tens position of the new result. We therefore induce that the next result will be 987,654. $\underline{Check\ Computation}$ Each computation includes 2 factors and an addend. The first factor is one digit longer than the first factor in the prior item in the sequence and contains the same leading digits as those in the first factor in the prior item in the sequence. The new trailing (ones) digit contains a value one greater than the trailing digit in the prior item in the sequence. $1\rightarrow12\rightarrow123\rightarrow1234\rightarrow12345\rightarrow123456$ The first factor in the next computation in the sequence will therefore be 123456. The second factor is 8 for every computation in the sequence. The addend the new computation is 1 greater than the addend in the prior computation. The addend in the next computation will be 6. The next computation in the sequence is $123456\times8+6=987648+6=987654$ This result agrees with the result derived by inductive reasoning.
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