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: 51

Answer

888,888 yes

Work Step by Step

$\underline{Inductive\ Reasoning}$ Each result in the sequence is a number containing the digit 8 in every position. The result of each computation in the sequence has one more digit than the prior result. Since the last result given is 88,888, a 5-digit number, we can induce that the next result will be a 6-digit number, 888,888. $\underline{Check\ Computation}$ 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 ones digit contains a value one less than the digit in the tens position. $9\rightarrow98\rightarrow987\rightarrow9876\rightarrow98765$ The first factor in the next computation in the sequence will therefore be 98765. The second factor is 9 for every computation in the sequence. The addend in each computation is one less than the addend in the prior computation. $7\rightarrow6\rightarrow5\rightarrow4\rightarrow3$ The addend in the next computation in the sequence will therefore be 3. The next computation in the sequence is $98765\times9+3=888885+3=888888$ This result agrees with the result derived by inductive reasoning.
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