Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-8 Geometric Sequences - Practice and Problem-Solving Exercises - Page 470: 24


The explicit formula is $a_{n}$=200 $\times$ ($\frac{1}{5}$$)^{n-1}$

Work Step by Step

You have to use the explicit formula. The explicit formula is $a_{n}$=$a_{1}$ $\times$ (r$)^{n-1}$. The starting value is 200, so it is $a_{1}$. You have the sequence 200,40,8 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{40}{200}$=$\frac{1}{5}$ and r=$\frac{8}{40}$=$\frac{1}{5}$.So the common ratio is $\frac{1}{5}$.Substitute the value of a1 and R into the explicit formula: The explicit formula is $a_{n}$=200 $\times$ ($\frac{1}{5}$$)^{n-1}$
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