Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 4 - An Introduction to Functions - 4-7 Sequences and Functions - Practice and Problem-Solving Exercises - Page 277: 10


Pattern: The previous term is being multiplied by $\frac{1}{2}$ The next two terms: $\frac{1}{2}$,$\frac{1}{4}$

Work Step by Step

The sequence: 8, 4, 2, 1, ... Finding the pattern: Difference between 1st and 2nd term: 2nd term-1st term=Difference 4-8=-4 Difference between 2nd and 3rd term: 3rd term-2nd term=Difference 2-4=-2 We see that the difference is not constant thus the sequence is not arithmetic. Thus we need to find the ratio between consecutive terms. Ratio of first and second term $\frac{Second term}{first term}$=Ratio =$\frac{4}{8}$ =$\frac{1}{2}$ Ratio of Second and third term $\frac{third term}{Second term}$=Ratio =$\frac{2}{4}$ =$\frac{1}{2}$ Ratio of Third and Fourth term $\frac{Fourth term}{third term}$=Ratio =$\frac{1}{2}$ =$\frac{1}{2}$ Therefore, the previous term is being multiplied by $\frac{1}{2}$ Finding the next two terms: Fifth term= Fourth term $ \times \frac{1}{2}$ = 1 $ \times \frac{1}{2}$ = $\frac{1}{2}$ Sixth term= Fifth term $ \times \frac{1}{2}$ = $\frac{1}{2}$ $ \times \frac{1}{2}$ = $\frac{1}{4}$ Therefore the next two terms are $\frac{1}{2}$ and $\frac{1}{4}$
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