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: 30


The recursive formula is $a_{1}$=100 and $a_{n}$=$a_{n-1}$ $\times$ ($\frac{1}{2}$).

Work Step by Step

Use the recursive formula $a_{1}$=a, $a_{n}$=$a_{n-1}$$\times$r. The starting value is 100 so it is the $a_{1}$ You have the sequence 100,50,25 so use the common ratio formula(r=$\frac{{a_{2}}}{{a_{1}}}$) r=$\frac{50}{100}$=$\frac{1}{2}$ and r=$\frac{25}{50}$=$\frac{1}{2}$.So the common ratio is $\frac{1}{2}$.Substitute the value of a1 and R into the recursive formula: The recursive formula is $a_{1}$=100 and $a_{n}$=$a_{n-1}$ $\times$ ($\frac{1}{2}$).
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