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: 14


Pattern: The previous term is being multiplied by 10 The next two terms: 20,000 and 200,000

Work Step by Step

The sequence: 2, 20, 200, 2000, ... Finding the pattern: Difference between 1st and 2nd term: 2nd term-1st term=Difference 20-2= 18 Difference between 2nd and 3rd term: 3rd term-2nd term=Difference 200-20=180 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 =$\frac{20}{2}$ =10 Ratio of Second and third term $\frac{third term}{Second term}$=Ratio =$\frac{200}{20}$ =10 Ratio of Third and Fourth term $\frac{Fourth term}{third term}$=Ratio =$\frac{2000}{200}$ =10 Therefore, the previous term is being multiplied by 10 Finding the next two terms: Fifth term= Fourth term $ \times$ 10 = 2000 $ \times$ 10 = 20,000 Sixth term= Fifth term $ \times$ 10 = 20,000 $ \times$ 10 = 200,000 Therefore the next two terms are 20,000 and 200,000
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