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 - Page 13: 72


The pattern $50$, $45$, $35$... Could have both $20$ and $15$ as the next number.

Work Step by Step

We need to write a list of numbers that has two patterns so that the next number in the list can be $15$ or $20$. There is more than one solution. One solution would be: $50$, $45$, $35$.... Here, we see that the second number is $5$ less than the first $(50-45=5)$. We also see that the third number is $10$ less than the second $(45 - 35 =10)$ Inductively, we could both conclude that the next number is calculated by: a. Subtracting $5$ more from the previous number to get this one than we did to get the previous number itself: $50-5=45$ we subtracted $5$ $45-10=35$ we subtracted $5$ more, for $10$ total This would make the next number: $35-15=20$ (we subtract $5$ more, for $15$ in total) b. Subtracting double what we previously subtracted: $50-5=45$ we subtracted $5$ $45-10=35$ we subtracted $2*5=10$ This would make the next number: $35-20=15$ (we subtracted $2*10=20$) This means that the next number in the pattern could be $15$ or $20$.
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